The Hyperbolic Field, Dark Matter and MOND

[Gary A]

The Hyperbolic Field, Dark Matter and MOND​

Many workers have verified the fact that General Relativity does indeed regard black holes as both physical and logical or mathematical singularities, which means that they are point masses having infinite density and infinitely deep gravitational wells. This means they have an asymptotic (to both the abscissa and ordinate) gravitational potential profile. As such, their overall physical geometry must be consistent with their nature as singularities, or else the term "singularity" has no meaning. Their actual gravitational potential profile must be represented by a hyperbola.

A Newtonian entity, however, must have a potential well that is represented by a parabola, i.e. its graph of distance (r) versus gravity (g) must actually pass through the origin and extend outward so that gravity declines to as near zero as one may like as r approaches a very large value, as it does at and beyond the periphery of spiral galaxies.

A hyperbolic potential must extend symmetrically, it is just the very nature of hyperbolas. Then, the decline in potential varies as 1/r, not 1/r^2 as a Newtonian object would. This echoes GR by saying that black holes do not exist in space, they define the space that they are in.

Milgrom and his version of MOND say that galaxies must behave in a non-Newtonian way: certainly. Does anyone have a fundamental problem with Milgrom’s raw data? We may quibble with his conclusion, but his observations are sound.

Let us hereby give a more parsimonious spin to the whole idea of MOND. In the bargain, we can explain Dark Energy sans quintessence and kill Dark Matter as well as Milgrom's demand for a reform of Newtonian Dynamics.

See citations or references at http://www.lonetree-pictures.net.

Saul Perlmutter and Adam Riess say that all previous research is a crock because theirs is the only good data that anyone has ever got. They do not intend this as a joke. Subsequent researchers just echo them because everyone must use the L/CDM model based on the FLRW metric and the Friedmann equations (editors insist). They all use the same model to predict the model. This is not mere retrodiction, it is circular reasoning yielding tighter curvature than the smallest draftsman's compass.

Alternative models have been developed, however, and the most faithful of these to general relativity do not support Dark Energy as any form a quintessence nor do they support Dark Matter. See the references.

Of course MOND has been criticized. This is one of the main points of this essay! MOND is unnecessary, but let us use the term "MOND effect" when referring to Milgrom's point concerning an additional very small residual gravitational acceleration constant that goes far beyond the peripheries of galaxies. After all, Milgrom is a careful worker. There is something here.
If it is not a revision to Newton's Law of Gravity, then it is the hyperbolic black hole gravitational potential effect. So, here is no need for Dark Matter as an alternative to MOND.

This MOND effect, when extended beyond galaxies to the global, not local, universe, Dark Energy is explained without invoking quintessence and so also, All traces of Dark Matter disappears. The above segment goes to the whole question of the exclusive use of a single model of the universe that depends on the Friedmann equations and the FLRW metric. The consensus interpretation of the Lambda/cold-dark-matter model must clearly be flawed if it leads to the conclusion that the scientific method must be scrapped in order to save the model. Dark Matter and Dark Energy as quintessence are ad hoc "add-ons" that are trying to find theoretical justification. We must not destroy the scientific method for their sakes.

Dark Energy as quintessence, in particular, is being called a supernatural or "unfalsifiable" hypothesis because no experiment can possibly directly challenge it, just like the existence of God hypothesis. Heretofore, all hypotheses must have adhered to the scientific method (the SM). Now, in order to admit Dark Energy quintessence, cosmologists insist that the SM must be tinkered with and an unfalsifiable hypothesis allowed for the first time in history. If we do this, the Pope can re-ascend to the Throne.

The total mass of the universe has been and still is open to question. The Matter/Energy that we can inventory accounts for only 4.5% of the total needed to "flatten" the anisotropy pattern that is seen in the Cosmic Microwave Background radiation (CMB). All of the indirect "overwhelming evidence" for expansion rate acceleration and Dark Energy as quintessence can be just as well applied to the concept that our inventory of matter and energy in our local universe is inadequate and that the mass of the global universe is at least 22.2 times as large as has been supposed (100%/4.5% = 22.2).

This proposed revision in the "total mass" and the General Relativity (GR) concept of the black hole hyperbolic field will save not only the SM, but the Friedmann Equations and the FLRW metric themselves too!

As far as dark matter is concerned, note that only what Milgrom says he discovered after carefully considering data from many many spiral galaxies is regarded seriuosly here. Also note that he ignores the fact that nearly all spiral galaxies, and most other types, have supermassive black holes embedded in them.

This makes a huge difference. Black holes and the whole associated mass of the galactic disk will behave like a non-Newtonian entity having a gravitational potential that falls off as 1/r, not as 1/r^2. Comparing a graph of this hyperbolic versus a Newtonian parabolic potential one sees that there is a virtually constant difference at large r. This is the source of Milgrom's residual centripetal acceleration constant that he says he sees in most of the galaxies he studied.

These facts do not argue with Milgrom's findings: far from it. They say his raw observations are probably right. But, he needs to consider the implications of the existence of relativistic supermassive black holes. His conclusion that Newton’s Law of Gravity needs to be revised is unnecessary.

Remember, these comments are just that, comments on the cosmological meaning of general relativity in regard to black holes in galaxies. Herein, any criticism of Dark Energy, per se, is irrelevant to the main point.

Milgrom proposes a new model for gravity. He calls it modified Newtonian dynamics (MOND). But, MOND will require a rewrite of general relativity, one of the most validated theories in all science (only quantum mechanics is better verified). These comments leave GR intact. The gist of them is simple, direct and jibes with the facts while being more parsimonious than MOND.

One does not observe the rotation of galaxies directly against the background of other galaxies. They rotate too slowly. One observes red-shifts from stars in different regions of each galaxy. Plotting rotational velocities got this way versus distance from the center of a galaxy, one should see a monotonic drop in velocity to near zero as one approaches large r. Instead, velocity reaches a constant nonzero plateau. This contradicts Newton's Law of Gravity. Milgrom accounts for this by tacking on a residual acceleration constant.

Okay, so Milgrom wants to add his tiny, residual acceleration constant to Newton's Law. But, all that this essay says is: it would be better to take into account the non-Newtonian hyperbolic black hole gravitational potential that simply must exist. This presence must exist in almost all spiral galaxies and also in other types of galaxies that may harbor black holes. It also means that the MOND residual acceleration constant is only an approximate fix to account for observations. It is really just an ad hoc phenomenological band-aid while the hyperbolic field effect is a physical and theoretical reality.

Galaxies that do not happen to show the MOND effect probably do not have supermassive black holes, they may contain more than one black hole, or else their black holes have formed so recently that there has not been enough time for the effect to propagate all the way to and beyond the periphery.

 

[OnlyMe]

The Hyperbolic Field, Dark Matter and MOND​

Many workers have verified the fact that General Relativity does indeed regard black holes as both physical and logical or mathematical singularities, which means that they are point masses having infinite density and infinitely deep gravitational wells....

This is a mathematically biased statement. While it is true that GR does mathematically reduce black holes to "point" singularities, the infinitely deep gravitational wells and thus infinite gravitational potential of such is not consistent with experience. Infinite remains infinite despite the method of reduction. We cannot just say and then something happens that changes things....

It is more likely that in practice a black hole does have volume and is not a point mass singularity. In which case the mathematics could be interpreted as definning an absolute mass density with volume rather than an absolute mass density "point singularity".

The gravitational interaction of a BH with the matter outside its event horizon falls off in the same manner as does the gravity of an ordinary star, planet or moon. We have no empirical evidence that the gravitational potential of a BH ever exceeds that requiring an escape velocity equivalent to $$c$$.

Mathematics is a tool. There are many things described mathematically that we do not find in experience, observation and experiment. Mathematics in and of itself is not physics. Only that portion of mathematics that describes experience and observation, is physics.., or rather a description of physics.

By framing your argument based on the theoretical point singularity, you introduce the potential for, not only and infinite mass density, but also an associated infinite mass. Which could theoretically support the underlying conclusions. But is is not consistent with observation, at all scales and distances.

It could be argued just as successfully that since GR describes space as dynamically interacting with matter/mass, and the Lense-Thirring or frame-dragging effect can be considered confirmed, that over time and regular orbital motions of the matter contained within a galactic system, the very weak interaction between matter and space responsible for the frame-dragging effect has a cumulative effect and that in mature galactic systems the involved space must be considered to be essentially inertially involved.

In such a circumstance, from within such a system the inertial aspect of the involved space would be unobservable, while from any frame of reference external to the galactic system it would be observed as a component of the orbital velocities of the involved galactic matter.

This too could be argued to be not only consistent with GR but also with a view of Newtonian dynamics, where space is a dynamic component of the whole system.

GR requires that space be dynamic and the Lense-Thirring or frame-dragging effect demonstrates that the dynamic nature of space cannot be limited to a cuvature we experience as gravitation.

The observed anomalies in the orbital velocities involving galactic rotation, are theirselves a problem of dynamics. A dynamic interaction from which the dynamic nature that GR bestows on space cannot be excluded from consideration.

No matter what trail we follow in an attempt to explain the involved anomolous observations, the inclusion of dark matter, MOND or viewing the whole as an inertial system composed of both matter and space, we are left with the same fundamental questions...

What is inertia and gravitation and how are they related or connected? Personnally I believe the answer will lie in a hybrid of GR and QM, that honors the success of both and yet may replace their conceptual projection into the world with an alternate perspective.

 

[Gary A]

Good thoughtful points

You make some good points to which I must respond:

1) The infinitely deep gravitational wells and thus infinite gravitational potential of such is not consistent with experience. Infinite remains infinite despite the method of reduction.

It is more likely that in practice a black hole does have volume and is not a point mass singularity.

2) We have no empirical evidence that the gravitational potential of a BH ever exceeds that requiring an escape velocity equivalent to $$c$$.

3) There are many things described mathematically that we do not find in experience, observation and experiment.

4) By framing your argument based on the theoretical point singularity, you introduce the potential for, not only and infinite mass density, but also an associated infinite mass. Which could theoretically support the underlying conclusions.

5) It could be argued just as successfully that since GR describes space as dynamically interacting with matter/mass, and the Lense-Thirring or frame-dragging effect can be considered confirmed, that over time and regular orbital motions of the matter contained within a galactic system, the very weak interaction between matter and space responsible for the frame-dragging effect has a cumulative effect and that in mature galactic systems the involved space must be considered to be essentially inertially involved.

6) In such a circumstance, from within such a system the inertial aspect of the involved space would be unobservable, while from any frame of reference external to the galactic system it would be observed as a component of the orbital velocities of the involved galactic matter.

This too could be argued to be not only consistent with GR but also with a view of Newtonian dynamics, where space is a dynamic component of the whole system.

GR requires that space be dynamic and the Lense-Thirring or frame-dragging effect demonstrates that the dynamic nature of space cannot be limited to a cuvature we experience as gravitation.

7) The observed anomalies in the orbital velocities involving galactic rotation, are theirselves a problem of dynamics. A dynamic interaction from which the dynamic nature that GR bestows on space cannot be excluded from consideration.

8) No matter what trail we follow in an attempt to explain the involved anomolous observations, the inclusion of dark matter, MOND or viewing the whole as an inertial system composed of both matter and space, we are left with the same fundamental questions...

What is inertia and gravitation and how are they related or connected? Personnally I believe the answer will lie in a hybrid of GR and QM.

Thanks again for taking the time to compose your reply.

1) At very least, the necessary experience is Milgrom’s raw observations. What other relevant hard experience do we have concerning purported actual black holes? The galactic rotation anomaly must be explained. Milgrom wants to modify Newtonian dynamics in a way that would vastly complicate general relativity. I want to introduce the simple expedient concept of the hyperbolic black-hole gravitational field effect, which preserves and even enhances GR. Which of us has the more extreme proposal?

Infinite remains infinite despite the method of reduction. This means that infinities cannot be explained away (the ultimate reduction). The existence of infinities in the Math surely has meaning. Schwartzchild thought so. He did not attempt to explain his infinities away.

Okay, there could be limits on the idea of infinity in this case. Perhaps there are quantum mechanical constraints such as the fact that pinpointing the center of a black-hole would violate the Heisenberg Uncertainty Principle. But, if a black hole compresses to a diameter as small as a Planck distance, it would serve the same purpose as an infinitely dense point mass. That is, there would be no way to tell that a black-hole was not infinitely dense. Milgrom’s observations indicate that it really does behave this way. Whether it may actually be so is a theoretical point that Schwartzchild has already considered.

I know that infinites are anathema to mathematicians. Their squeemishness is misplaced in cosmology, however. What if it happens that it is actually more likely that a BH is a real point mass, as close as we can tell by QM, having as near to an infinite density that may be required to provide the proper effect (the real meaning of “infinite”).

2) Actually, this is irrelevant. We are speaking of the geometry of BHs and the influence this geometry must have on the structure of spacetime in the vicinity. The consequences are to be determined by observation and experiment. If the escape velocity does not actually exceed c nearer to the center of a BH, then there is no such thing as an event horizon anyway. Karl Schwartzchild would object. If the escape velocity may be exceeded only by a smidgen determined by the Heisenberg Principle, why not by something rather more than just a smidgen? We need only to suppose that the effective radius of a BH is small enough to produce the required effect, which we may then consider to approach that needed to give effectively infinite density. “Effectively” is the keyword.

3) The nausea experienced by some professional mathematicians upon contemplation of infinity is not matched by the feelings of some others who revel in the concept. In fact, there is a whole branch of mathematics devoted to it. I do not believe that professionals would devote their whole careers to studies that do not have even theoretical practical consequences. Math is beautiful, but is no “10”. And, it is a whore.

The mathematics of infinities engendered by the Schwartzchild analysis of GR serve as a flag signaling that there is something going on here. What we find in experience now does not equate to what may be found in the future. And, Milgrom’s observations are still extant. No revision of Newton’s Law of Gravity is needed. No Dark Matter is needed either (Dark Matter is based on Milgrom). Just a liberal tweak upon the concept of what it really means to be a black hole is all that is required. Sometimes liberalism makes sense.

4) Speaking of infinite mass, one would have to refer to the whole universe, at minimum. What if BHs are wormholes leading to this very same universe, but from a different perspective? Might it not then have an effectively infinite mass? But this is all an unnecessary complication. The potential need not be realized.

5) Okay. Now we have another possible alternative to Dark Matter.

6) Well, of course. Do we not always observe external galaxies from afar? It seems far fetched that we should ever observe the Milky Way from beyond. So, your idea means that it should be futile to try to detect the effect in our own galaxy. But, is not GR all about the curvature of spacetime and the dynamic effects that we can expect from such a curvature. Remember, the vector and tensor math of GR is derived from techniques used in hydrodynamics. The dynamic nature of fluids has a “frame dragging” equivalent. In other words, you are saying that GR is dynamic, not static. Even Newtonian “dynamics” is really static in nature because it cannot treat transitions between states which are time dependent. Time dependent variations between fluid states is often referred to as “turbulence”. Is there “turbulence” in the behavior of spacetime?

7) You amplify your comment that frame dragging style wrinkles on the face of GR could explain MOND and explain away Dark Matter. What if BOTH these wrinkles and the giant scar of the hyperbolic field effect should apply?

8) Wonderful. Fundamental questions are what science is all about. But, the anomalies do indeed need to be explained.

Good luck finding a valid hybrid of GR and Quantum. Instead of M Theory, maybe we can call it OM Theory.

Thanks for taking the time to read this. Further response would be appreciated.

 

[Gary A]

MOND, inflation, acceleration of universe expansion rate and eschatology (fate)

MOND, inflation, acceleration of universe expansion rate and eschatology (fate)​

Presumably, when the universe formed from Alan Guth's inflaton, its "hyperbolic" (F = GmM/rr) gravitational field began to collapse into a parabolic one (F = GmM/r^2). See posts elsewhere.

That transition or collapse continues to this day. But, certainly the process is almost done. There cannot be an infinite amount of gravitational energy sequestered in the hyperbolic (proportional to 1/r) field that would be available to fuel acceleration of the expansion rate via such a transformation. That is, transition to a lower energy parabolic (proportional to 1/r^2) field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the mainspring has almost run down by now.

If the expansion rate is called h, and its present value is called P, then h = P at any given time, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression, P = hoe^(-rt), where ho is an initial value for the expansion rate, h, r is the rate of increase in this expansion and t is time.

We can get an estimate of a value for h0 from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P1, and acceleration rate, r, are observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = R0e^(rt), where R is the putative “radius” or scale factor of the universe.

The current value (at t = 1) of the expansion rate is H0, the Hubble “constant”, so P1 = H0.

Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. The hyperbolic curve levels off near zero and continues to subside gently almost linearly for an indefinite time. The current state of the universe may be consistent with this dormant period. The conclusion here is that acceleration may continue for a long time while slowly decreasing nearer to zero. In other words, even with acceleration of the expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

The point made about point masses and singularities engendering a hyperbolic gravitational field is a mathematical necessity. Consider what a point mass as a singularity actually means. If it does not mean that they generate a hyperbolic gravitational field, then the words point mass and singularity are meaningless. Karl Schwartzchild would not agree with this negation of his analysis of general relativity.

Some say that general relativity predicts that black-hole singularities must possess a gravitational field that falls off as 1/r^2 with no difference from other Newtonian entities. I don’t believe general relativity says this under the rule that a black-hole must contain or “be” a singularity. If treated as a singularity, black-holes must have a hyperbolic gravitational potential. This is a geometric necessity. Such a gravitational potential falls off as 1/r.

In association with the galactic disk which may have a coincident and coaxial gravitational field equivalent to a couple of hundred billion sols, the residual hyperbolic field at large r generates with Milgrom’s extra gravitational acceleration seen near the periphery of galaxies, the main impetus for Dark Matter. The periphery is a self defining zone that is responsible for Milgrom’s leftover acceleration “constant” that he wants to tack onto Newton’s Law. The present observations mean that Milgrom’s MOND is unnecessary. And, Dark Matter is superfluous too because all the phenomena associated with Dark Matter are explained equally well by the hyperbolic field effect.

The MOND effect itself is evidence for the hyperbolic 1/r field. Certainly, there will be other sources of confirmation.

 

[Gary A]

MOND, modified Newtonian dynamics

Mordechai Milgrom carefully analyzed a statistically robust number of spiral and other galaxies plus many galactic clusters. He discovered a strange leveling of the galactic rotational velocity distribution. He found the same effect in almost all the galaxies he studied. The ones that did not have the effect may have not yet developed proper structures, especially in their cores, or had not yet had time for Milgrom's own assumed galactic gravitational field effects to propagate all the way to the periphery and beyond. See http: //www lonetree-pictures net, sub-site MOND for a more detailed treatment.

A caveat - a graphic of a whiteboard mathematical presentation is given at the above website of the MOND effect compared with the nearly identical hyperbolic field effect. The following warning is mentioned in the text but not in the graphic. Newton's Law of Gravity that applies to the black hole galactic gravitational field might have a term in 1/r, not 1/r^2. This messes-up any dimensional analysis that one may like to do to verify the math. So, as mentioned in the text, one may include a fix. Use 1/rr where r is the unit vector of r, retaining its dimension. Then 1/rr will have the same absolute value as plain 1/r but dimensionally, 1/rr will be perfectly consistent with Newton's Law.

Dark Matter is discussed there and the paper disagrees with Milgrom's call for modification of Newtonian dynamics (MOND). Dark Energy at http: //www lonetree-pictures net is also explained by extrapolation of Milgrom's discovery to Alan Guth's Inflationary "inflaton" particle which even Guth will agree must have possessed a singular hyperbolic black-hole gravitational field PRIOR to the first instants of the inflationary process. No quintessence is required.

The unique ultra massive black-hole gravitational field began to collapse at this instant and must still be collapsing - transitioning to a more purely Newtonian field. In the process, its time dependent transition may generate relativistic perceptual effects that mimic contributions to what has been called "acceleration" or "dark energy". ALL the "overwhelming" evidence for dark energy and acceleration can be parsimoniously subsumed under the heading of this kind of black-hole gravitational field effect according to the Critique of the Universe sub-site.

Milgrom does indeed propose a new model for gravity. He calls it modified Newtonian dynamics (MOND). But, MOND will require a rewrite of general relativity, one of the most validated theories in all science (only quantum mechanics is better verified). The following comments leave GR intact. The gist of them is simple, direct and jibes with the facts while being more parsimonious than MOND.

Note that one does not observe the rotation of galaxies directly against the background of other galaxies. They rotate too slowly. One observes red-shifts from stars in different regions of each galaxy. Plotting rotational velocities got this way versus distance from the center of a galaxy, one should see a monotonic drop in velocity to near zero as one approaches large r. Instead, velocity reaches a constant nonzero plateau. This contradicts Newton's Law of Gravity. Milgrom accounts for this by tacking on a residual acceleration constant.

Okay, so Milgrom wants to add his tiny, residual acceleration constant to Newton's Law. But, all that this note says is that it would be better to take into account the non-Newtonian hyperbolic black hole gravitational potential that simply must exist in almost all spiral galaxies and also in other types of galaxies that may harbor black holes. It also means that the MOND residual acceleration constant is only an approximate fix to account for observations. It is really just an ad hoc phenomenological band-aid while the unique black-hole gravitational field effect is both a physical and theoretical reality.

Galaxies that do not happen to show the MOND effect probably do not have supermassive black holes, they may contain more than one black hole, or else their black holes have formed so recently that there has not been enough time for the effect to propagate all the way to and beyond the periphery. Milgrom’s residual acceleration constant, a0, may be due to the fact that he always studied stars near the periphery of galaxies. This is a self-selecting constraint that always would yield the same value for a0

 

[Gary A]

MOND, modified Newtonian dynamics

Mordechai Milgrom carefully analyzed a statistically robust number of spiral and other galaxies plus many galactic clusters. He discovered a strange leveling of the galactic rotational velocity distribution. He found the same effect in almost all the galaxies he studied. The ones that did not have the effect may have not yet developed proper structures, especially in their cores, or had not yet had time for Milgrom's own assumed galactic gravitational field effects to propagate all the way to the periphery and beyond. See http: //www lonetree-pictures net, sub-site MOND for a more detailed treatment.

A caveat - a graphic of a whiteboard mathematical presentation is given at the above website of the MOND effect compared with the nearly identical hyperbolic (F = GmM/rr) field effect. The following warning is mentioned in the text but not in the graphic. Newton's Law of Gravity that applies to the black hole galactic gravitational field might have a term in 1/r, not 1/r^2. This messes-up any dimensional analysis that one may like to do to verify the math. So, as mentioned in the text, one may include a fix. Use 1/rr where r is the unit vector of r, retaining its dimension. Then 1/rr will have the same absolute value as plain 1/r but dimensionally, 1/rr will be perfectly consistent with Newton's Law.

Dark Matter is discussed there and the paper disagrees with Milgrom's call for modification of Newtonian dynamics (MOND). Dark Energy at http: //www lonetree-pictures net is also explained by extrapolation of Milgrom's discovery to Alan Guth's Inflationary "inflaton" particle which even Guth will agree must have possessed a singular hyperbolic black-hole gravitational field PRIOR to the first instants of the inflationary process. No quintessence is required.

The unique ultra massive black-hole gravitational field began to collapse at this instant and must still be collapsing - transitioning to a more purely Newtonian field. In the process, its time dependent transition may generate relativistic perceptual effects that mimic contributions to what has been called "acceleration" or "dark energy". ALL the "overwhelming" evidence for dark energy and acceleration can be parsimoniously subsumed under the heading of this kind of black-hole gravitational field effect according to the Critique of the Universe sub-site.

Milgrom does indeed propose a new model for gravity. He calls it modified Newtonian dynamics (MOND). But, MOND will require a rewrite of general relativity, one of the most validated theories in all science (only quantum mechanics is better verified). The following comments leave GR intact. The gist of them is simple, direct and jibes with the facts while being more parsimonious than MOND.

Note that one does not observe the rotation of galaxies directly against the background of other galaxies. They rotate too slowly. One observes red-shifts from stars in different regions of each galaxy. Plotting rotational velocities got this way versus distance from the center of a galaxy, one should see a monotonic drop in velocity to near zero as one approaches large r. Instead, velocity reaches a constant nonzero plateau. This contradicts Newton's Law of Gravity. Milgrom accounts for this by tacking on a residual acceleration constant.

Okay, so Milgrom wants to add his tiny, residual acceleration constant to Newton's Law. But, all that this note says is that it would be better to take into account the non-Newtonian hyperbolic black hole gravitational potential that simply must exist in almost all spiral galaxies and also in other types of galaxies that may harbor black holes. It also means that the MOND residual acceleration constant is only an approximate fix to account for observations. It is really just an ad hoc phenomenological band-aid while the unique black-hole gravitational field effect is both a physical and theoretical reality.

Galaxies that do not happen to show the MOND effect probably do not have supermassive black holes, they may contain more than one black hole, or else their black holes have formed so recently that there has not been enough time for the effect to propagate all the way to and beyond the periphery. Milgrom’s residual acceleration constant, a0, may be due to the fact that he always studied stars near the periphery of galaxies. This is a self-selecting constraint that always would yield the same value for a0

 

[Gary A]

The Universe for Idiots

Yes, reference is made to Alan Guth's Inflation hypothesis. Refer also to black holes as "huge" singularities only insofar as their masses must be huge.

From Wikipedia under "Schwartzchild Metric":

"The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant;

(which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes."

I simply make the observation that the so-called MOND effect itself can better be explained by the simple expedient of introducing the hyperbolic (proportional to 1/rr) black hole (HBH) galactic gravitational field. MOND doesn't explain anything. As presented by Milgrom, it is an unnecessary complication.

Extrapolated to the entire universe, the HBH field effect serves as a mechanism whereby a continuing transition from a hyperbolic 1/rr field to a parabolic (proportional to 1/r^2) gravitational field can provide energy to cause accelerated expansion of the universe. It is a mechanism whereby a positive cosmological constant can be achieved without any fuss, that is, without quintessence.

Read the books Inflation by Alan Guth and The Fabric of the Cosmos by Brian Greene.

The theory of inflation postulates that there was something before the Big Bang. It is the "inflaton" particle which sprang into existence at a high energy by quantum mechanical fluctuation. Along with the inflaton, there must have been a gravitational field. This field must have been one whereby F = |GmM/rr|, having a hyperbolic gravitational field profile. Normally, a Newtonian entity would have a parabolic (F = GmM/r^2) gravitational field profile. But the inflaton is the mother of all black-holes, or MOAB. As a black-hole, the inflaton MOAB must have had a hyperbolic (proportional to 1/|rr|) gravitational field because it is a point mass having only a center but zero radius. Zero within the bounds of the Heisenberg uncertainty principle, that is. The symbol r is the unit vector associated with r, the radial distance to the center in graphs like the field profile. This unit vector makes dimensional analysis work nicely. It is a constant, so the related equation for F is the equation for a hyperbola.

This has consequences because when the inflaton particle suddenly began to decay into the matter and energy we see today, the hyperbolic field began to decay as well. It began to transform into a parabolic (proportional to 1/r^2) gravity field because it was no longer a point-particle having zero radius. The profile of a hyperbolic gravitational field implies inherently higher energy than the equivalent parabolic field profile. So, as the hyperbolic field transitioned to a parabolic one, it released (and continues to release) its potential energy.

This potential energy fueled and continues to fuel acceleration of the expansion rate of the universe (Hubble expansion). This acceleration effect is sometimes referred to as being due to Dark Energy. It is often suggested that Dark Energy stems from a fundamental new force, to be called "quintessence", but it could really be due to a gravitational effect as described here. A gravitational effect is called "Lamda", for Einstein's cosmological constant that he added to his general theory of relativity. Lamda has a positive value because decay of the hyperbolic (1/|rr|) field releases energy into the observable universe.

Look up the FLRW metric and the Friedmann equations as well as the Big Bang and Guth's inflation on the Internet. Wikipedia is a good place to start.

 

[Gary A]

whiteboard presentation of the hyperbolic black-hole gravitational field effect

http://www.lonetree-pictures.net/MOND & HBH .htm

see this image for a whiteboard presentation of the hyperbolic black-hole gravitational field effect and its relation to MOND. It IS MOND!

It is intended as the main slide in a lecture presentation. Therefore, it is not complete without more explanation

 

[Gary A]

whiteboard presentation of the hyperbolic black-hole gravitational field effect

http://www.lonetree-pictures.net/MOND & HBH .htm

whiteboard presentation of the hyperbolic black-hole gravitational field effect and its relation to MOND. It IS MOND!

It is intended as the main slide in a lecture presentation. Therefore, it is not complete without more explanation

 

[Gary A]

The new cosmos and the hyperbolic field hypothesis for mond

THE NEW COSMOS
AND THE
HYPERBOLIC FIELD HYPOTHESIS FOR MOND
(modified Newtonian Dynamics)

Mathematical, graphical models of the Universe according to the Black-Hole and
Hot Big Bang Theories using "extensive variables" and therefore giving new insights​

Albert Einstein easily derived a relativistic differential equation that was guaranteed to reproduce Newton's Law when it was integrated with certain simplifying assumptions. He could have written a differential equation that reproduced MOND, but he didn't. He just didn't. He had no reason to do so because the various MOND observations had not yet been made.

But, considering the very definition of a black-hole, it must be accompanied by a very characteristic and very different gravitational field. Because it is a singularity, a single point-object with infinite density, it must possess a gravitational field that is determined by its single point, its singular property. Its gravitational field graphical potential plot must therefore approach an asymptote (boundary line having a limiting value) at radius = 0 and, by symmetry, it must approach another (perpendicular) asymptote at radius = infinity. This is consistent with the definition of a hyperbolic field, not one that follows Newton's inverse square law, which is parabolic in nature. A hyperbola follows an inverse law, 1/r while a parabola follows an inverse square law, 1/r^2.

http://www.lonetree-pictures.net/MOND & HBH .htm
Whiteboard presentation of the development of the hyperbolic black-hole gravitational field effect​

If black-holes posses hyperbolic gravitational fields, then there is no mystery in MOND. Look at this image of a whiteboard derivation of the hyperbolic black-hole (HBH) gravitational acceleration and velocity profile near a galaxy containing a supermassive black-hole at its center. On the whiteboard, I also have written a synopsis of the MOND development.

For MOND, Newtonian gravitational acceleration is denoted aN. The variant acceleration due to MOND expresses aN in terms of an acceleration that is modified by the function μ(a/a0), which is equal to 1 when the radius from the center is small enough for the overall gravitational acceleration to be large relative to the MOND constant, a0. When the putative acceleration is small relative to a0, μ is equal to a0 such that the equations on the lower left are satisfied. This happens when radius r is large enough for a2/a0 = aN = GM/r, and the total force of gravitational attraction enters the MOND regime. These values for r are equal to and beyond the point where the velocity distribution of stars encircling the galaxy in its outer regions becomes constant.

Remember M2 = the supermassive black-hole mass while M1 = mass of the stars in the disk inside the radius r, to a given star. This radius might enclose more than 95% of all the stars in the disk and so may as well be considered to enclose all of them. But, a graphical model would have to take the percent enclosure into account in order to plot a theoretical velocity distribution. So, it will be a little while before I actually do this.

According to Newton’s inverse square law, velocities should fall off rapidly toward zero in this outer zone. But, observations show that it does not. Instead, they fall off much more slowly and become constant according to the vMOND equation on the lower right.

But, the hyperbolic field contribution to the overall galactic gravitational field shown as the blue curve, y1, in the graph above, gives precisely the same result. Thus, vMOND = vHBH. If it is admitted that black-holes are different, that they have special properties, among them that they are gravitational singularities, then this is not too surprising. In fact, it should have been thought of before, and it probably has. But, it is now being overlooked. I hope this effort on my part may prevent this oversight from being propagated indefinitely.

Note that the usual depiction of the velocity profile of a spiral galaxy shows velocities rising to a maximum as one moves toward the center whereupon they fall off virtually to zero as one gets very close to r = 0. My simpler velocity distribution profile is for just one or for a very few stars. The standard picture of a maximum and fall-off in velocity occurs because stars get crowded as one approaches the center and their orbital paths become chaotic. As one moves in, just as many stars move clockwise as move counterclockwise (and on more nearly perpendicular trajectories relative to the galactic plane) and the net velocity declines. The stellar distribution becomes more spheroidal too, resulting in the classic galactic “bulge”. When I formulate my model, I will have to take all this into account as well. This is going to be fun.

It is interesting to imagine what a galaxy would look like if purely Newtonian F = ma = GMm/r^2 ≠ GMm/r for large r. Then, v∞ ≠ (GM)1/2 = constant. Instead, rotational velocity would fall off toward zero as r increases without bound. The stars would lag further and further behind and the spiral arms would wrap around the center much more tightly, like the mainspring of an old windup clock. So, one can see the MOND effect by just looking:

This means that there may well be no such thing as dark matter or twin matter or any such Baroque complications festooning the simple picture of the universe that we, as scientists, should be looking for. It is in the nature of human beings to overdo. Dark matter and MOND are in danger of becoming vastly overdone.

So, now let me engage in a little bit of my own overdoing.

If this version of MOND is correct, there will never be a measurement of a0 obtained in the laboratory in a supersensitive Cavendish experiment. That is, not unless we can produce a sufficiently long-lived black-hole in the lab. This prediction will not go over very well with a lot of people, so it will not be readily accepted.

In elliptical and globular galaxies wherein the MOND effect may be observed, HBH MOND will require that one or more supermassive black-holes shall be found, naked black-holes at that. The intragalactic black-hole presence in galactic clusters and superclusters may not be enough to account for MOND in these objects either, so some naked black holes may well be found embedded within them too. Nobody is looking for them now, so it is not surprising that they have not yet been found.

The hyperbolic field concept can be extended to the entire universe, too. If it can be verified, it may go a long way toward an accounting for the mistaken interpretations of acceleration and dark energy in the universe. This would require that the primordial black-hole, the mother of all black-holes or MOAB, must have persisted in some form, probably diminished, for a long time after it started to decay into the universe that we see now. In other words, the highly excited inflaton particle may have taken some time to deconvolve, decompose and collapse so, remnants may even still persist today.
If weird science is needed to justify funding, this is it.

The Hyperbolic Black-Hole Field Anomaly​

Supermassive black-holes pervade the universe. In the field of our view, within the light cone of our observational limit, there are over 200 billion supermassive black holes residing at the centers of large galaxies. There are probably many more large naked black holes residing in enormous dust clouds or simply standing alone as bald singularities in elliptical galaxies and globular clusters and within galactic clusters and superclusters. These invisible black-holes simply have not had enough time to accumulate a large cloak of glowing matter that emits light by virtue of its in-fall to their event horizons. Therefore, they are truly black.

Black-holes and their hyperbolic gravitational fields fully account for the dark matter necessary to keep galaxies spinning at their observed rates and to bind galactic clusters and superclusters. If there are large enough numbers of such black holes to do this job, then the assumption of the Cosmological Principle is dead wrong by this fact alone.

It is as though the universe is made of Swiss cheese and we have assumed it is made of white cheddar. It is well known that a medium filled with small bubbles or tiny solid particles behaves very differently toward the propagation of any type of energy through it. Numerous small bubbles, for instance, lower the speed of sound and affect the way a medium like water absorbs microwaves. In fact, shock waves propagate so differently that the behavior of the explosion front in the conventional chemical explosive has to be taken into account in the design of nuclear weapons. Bubbles and dispersed solids must be avoided.

When assumptions are made regarding the type of “perfect fluid” of which the universe is made we cannot disregard exceptional circumstances like the presence of a froth of black-holes embedded within it. It matters little that there are good reasons for using approximations like the Cosmological Principle. After all, something must be done to allow the formulation of comprehensible theory giving the means for tractable calculation. But, this theory and such calculation must be regarded as only approximate.
Unless steps are taken to greatly refine theory and bring calculations up to a much higher standard, there shall be no such thing as “precision cosmology”.

The hyperbolic black-hole (HBH) gravitational fields, stemming from supermassive black-holes at the centers of galaxies, extend far beyond the visible boundaries of the galaxies themselves. The Modified Newtonian Dynamics (MOND) effect shows that these fields may be virtually infinite in extent. If this is so, the spacetime continuum that is actually present in the universe is very different from the one that Einstein assumed.

These oversimplifications are implicit in the Friedmann LeMaitre Robertson Walker metric that Friedmann used to formulate the form of the General Relativity equations that cosmologists commonly use. In other words, the whole structure upon which is built the argument for acceleration of the rate of expansion of the universe and the existence of dark energy (not to mention dark matter) is deeply suspect.

It is just too bad, so sad, that so many physicists have devoted whole careers to mastering the mathematics of General Relativity from the perspective of the FLRW metric and the Friedmann equations. These anachronistic personalities will simply have to die off or permanently retire before we can make progress. After all, there is some truth in the saying about physicists who see everything in terms of some simplifying assumption. But "First, we assume a perfect sphere." is not how to do critical science deserving of massive funding.

Only spacetime itself is homogeneous and isotropic. But, once it becomes filled with supermassive black-holes and other dark naked singularities, it cannot be treated this way with any degree of precision or accuracy. Some investigators have already picked up on this fact. They are formulating new cosmologies with different metrics and are abandoning the oversimplified assumptions that were designed to make calculations easy. Much too easy. They have come to appreciate the power of supercomputers and advanced mathematical logic programs to handle more realistic models of the universe. This twenty-first century trend is only just beginning. The real revolution in cosmology has yet to come. It will be a counterrevolution, for the twentieth century is dead.

The Hyperbolic Field and Dark Matter​

Many workers have verified the fact that General Relativity does indeed regard black holes as both physical and logical or mathematical singularities, which means that they are point masses having infinite density and infinitely deep gravitational wells. This means they have an asymptotic (to both the abscissa and ordinate) gravitational potential profile. As such, their overall physical geometry must be consistent with their nature as singularities, or else the term "singularity" has no meaning. Their actual gravitational potential profile must be represented by a hyperbola.

A Newtonian entity, however, must have a potential well that is represented by a parabola, i.e. its graph of distance (r) versus gravity (g) must actually pass through the origin and extend outward so that gravity declines to as near zero as one may like as r approaches a very large value, as it does at and beyond the periphery of spiral galaxies.

A hyperbolic potential must extend symmetrically, it is just the very nature of hyperbolas. Then, the decline in potential varies as 1/r, not 1/r^2 as a Newtonian object would. This echoes GR by saying that black holes do not exist in space, they define the space that they are in.

Milgrom and his version of MOND say that galaxies must behave in a non-Newtonian way: certainly. Does anyone have a fundamental problem with Milgrom’s raw data? We may quibble with his conclusion, but his observations are sound.

Let us hereby give a more parsimonious spin to the whole idea of MOND. In the bargain, we can explain Dark Energy sans quintessence and kill Dark Matter as well as Milgrom's demand for a reform of Newtonian Dynamics.

See citations or references at http://www.lonetree-pictures.net.

Saul Perlmutter and Adam Riess say that all previous research is a crock because theirs is the only good data that anyone has ever got. They do not intend this as a joke. Subsequent researchers just echo them because everyone must use the L/CDM model based on the FLRW metric and the Friedmann equations (editors insist). They all use the same model to predict the model. This is not mere retrodiction, it is circular reasoning yielding the more curvature than the smallest draftsman's compass.

Alternative models have been developed, however, and the most faithful of these to general relativity do not support Dark Energy as any form a quintessence nor do they support Dark Matter. See the references.

Of course MOND has been criticized. This is one of the main points of this essay! MOND is unnecessary, but let us to use the term "MOND effect" when referring to Milgrom's point concerning an additional very small residual gravitational acceleration constant that goes far beyond the peripheries of galaxies. After all, Milgrom is a careful worker. There is something here.
If it is not a revision to Newton's Law of Gravity, then it is the hyperbolic black hole gravitational potential effect. There is no need for Dark Matter.

This MOND effect, when extended beyond galaxies to the global, not local, universe, Dark Energy is explained without invoking quintessence and so, Dark Matter disappears. The above segment goes to the whole question of the exclusive use of a single model of the universe that depends on the Friedmann equations and the FLRW metric. The consensus interpretation of the Lambda/cold-dark-matter model must clearly be flawed if it leads to the conclusion that the scientific method must be scrapped in order to save the model. Dark Matter and Dark Energy as quintessence are ad hoc "add-ons" that are trying to find theoretical justification. We must not destroy the scientific method for their sakes.

Dark Energy as quintessence, in particular, is being called a supernatural or "unfalsifiable" hypothesis because no experiment can possibly directly challenge it, just like the existence of God hypothesis. Heretofore, all hypotheses must have adhered to the scientific method (the SM). Now, in order to admit quintessence, cosmologists insist that the SM must be tinkered with and an unfalsifiable hypothesis allowed for the first time in history. If we do this, the Pope can re-ascend to the Throne.

The total mass of the universe has been and still is open to question. The Matter/Energy that we can inventory accounts for only 4.5% of the total needed to "flatten" the anisotropy pattern that is seen in the Cosmic Microwave Background radiation (CMB). All of the indirect "overwhelming evidence" for expansion rate acceleration and Dark Energy as quintessence can be just as well applied to the concept that our inventory of matter and energy in our local universe is inadequate and that the mass of the global universe is at least 22.2 times as large as has been supposed (100%/4.5% = 22.2).

This proposed revision in the "total mass" and the General Relativity (GR) concept of the black hole hyperbolic field will save not only SM, but the Friedmann Equations and the FLRW metric themselves too!

As far as dark matter is concerned, note that only what Milgrom says he discovered after carefully considering data from many many spiral galaxies is reported here. Also note that he ignores the fact that nearly all spiral galaxies, and most other types, have supermassive black holes embedded in them.

This makes a huge difference. Black holes and the whole associated mass of the galactic disk will behave like a non-Newtonian entity having a gravitational potential that falls off as 1/r, not as 1/r2. Comparing a graph of this hyperbolic versus a Newtonian parabolic potential one sees that there is a virtually constant difference at large r. This is the source of Milgrom's residual centripetal acceleration constant that he says he sees in most of the galaxies he studied.

These facts do not argue with Milgrom's findings: far from it. They say he is probably right. But, he needs to consider the implications of the existence of relativistic supermassive black holes. His conclusion that Newton’s Law of Gravity needs to be revised is unnecessary.

Remember, these comments are just that, comments on the cosmological meaning of general relativity in regard to black holes in galaxies. Herein, any criticism of Dark Energy, per se, is irrelevant to the main point.

Milgrom proposes a new model for gravity. He calls it modified Newtonian dynamics (MOND). But, MOND will require a rewrite of general relativity, one of the most validated theories in all science (only quantum mechanics is better verified). The following comments leave GR intact. The gist of them is simple, direct and jibes with the facts while being more parsimonious than MOND.

Note that one does not observe the rotation of galaxies directly against the background of other galaxies. They rotate too slowly. One observes red-shifts from stars in different regions of each galaxy. Plotting rotational velocities got this way versus distance from the center of a galaxy, one should see a monotonic drop in velocity to near zero as one approaches large r. Instead, velocity reaches a constant nonzero plateau. This contradicts Newton's Law of Gravity. Milgrom accounts for this by tacking on a residual acceleration constant.

Okay, so Milgrom wants to add his tiny, residual acceleration constant to Newton's Law. But, all that this essay says is it would be better to take into account the non-Newtonian hyperbolic black hole gravitational potential that simply must exist in almost all spiral galaxies and also in other types of galaxies that may harbor black holes. It also means that the MOND residual acceleration constant is only an approximate fix to account for observations. It is really just an ad hoc phenomenological band-aid while the hyperbolic field effect is a physical and theoretical reality.

Galaxies that do not happen to show the MOND effect probably do not have supermassive black holes, they may contain more than one black hole, or else their black holes have formed so recently that there has not been enough time for the effect to propagate all the way to and beyond the periphery.

 

[Gary A]

See "Gary A's Critique of the Universe ( 1 2)", especially Gary's latest update.

 

[Gary A]

The Scientific Method and Quintessence

The Scientific Method and Quintessence​

The scientific method requires scientists and all others who claim to think rationally to answer knotty questions by means of experiment (or careful observation). In order to do this effectively, one must formulate a hypothesis, a statement of the putative principle that engages all the known implications. These implications must be rather direct. Circumstantial consequences are just that - circumstantial and cannot PROVE a hypothesis. Those better former implications must suggest experiments that will verify them or not. It is good if there are direct elements of principle and subservient implications of the hypothesis. It is better if a complete and utter negative statement of the hypothesis can be formulated. Then, the net sum of the original hypothesis and the negative hypothesis should be zero. Logically, the negative completely cancels the positive hypothesis. This negative hypothesis is called the "null" hypothesis because it would nullify the other if it proves to be true and it would tend to validate the positive hypothesis, at least it would fail to PROVE it false, if it was shown to be false in any way. Then, if direct evidence can be found that tends to corroborate the original positive hypothesis, we can begin to regard it as a good logical beginning. THEN, if this positive hypothesis can be combined with statements that have already been proven and the combined implications can be verified, we have the beginnings of proof.

The key to this process is our ability to form an experimentally testable Null Hypothesis. The evidence FOR the positive statement of the hypothesis is insufficient in itself because circumstances may combine to fool our little experiments. We are human. If an appropriate robust Null Hypothesis cannot be formulated, the original hypothesis is unsuitable to merit the attention of the scientist.

This is relevant to the debates about Dark Energy, quintessence and Dark Matter. Dark energy is the reservoir of potential energy that is supposed to exist as an underlayment or foundation of the universe. Quintessence is supposed to be a new force field that is just another component of the universe. All fundamental force fields have an associated particle. So, if there is quintessence, there should be a quintessence particle also. Invisible Dark Matter is supposed to account for the anomalous rotation velocity distribution seen in galaxies and galactic clusters.

To call one's self a scientist, one must respect the scientific method. It is not a scientist's dogma any more than is it such to follow a firefighter's code; one must respect the power of fire - or else you die.

An unfalsifiable hypothesis has no business occupying the time of the scientist. Whole theories have often been constructed from unfalsifiable hypotheses. Such theories are often fun to think about, even edifying and inspiring - but they certainly are not science.

There is a place for faith. But, if a person of faith needs experimental proof, he will have little of either. We all need faith. We all use faith in some way. In times of trouble and sorrow, sometimes it is all we have. God loves us, we believe. Our belief makes it so. If we can say sincerely that a principle of human conduct or relations should be true, then it is. Human reality is what we can say it should be. This is called Primary Christian Existentialism. All men and women of faith are Christian existentialists.

All scientists hew to a code of honor as well as to the scientific method. Truth is not just a buzzword. Truth is meaning. Truth is the scientist's life. Truth is noble.

In a very real sense, to the scientist, "Truth" is the next best thing to God.

 

[Gary A]

The Hyperbolic Field

The Hyperbolic Field, Dark Matter and MOND​

A hyperbolic potential must extend symmetrically, it is just the very nature of hyperbolas. Then, the decline in potential varies as 1/r, not 1/r^2 as a Newtonian object would. This echoes GR by saying that black holes do not exist in space, they define the space that they are in.

Milgrom and his version of MOND say that galaxies must behave in a non-Newtonian way: certainly. Does anyone have a fundamental problem with Milgrom’s raw data? We may quibble with his conclusion, but his observations are sound.

Remember, I have corrected the following item.

For the hyperbolic field all equations are related to F = GMm/rr1, NOT = GMm/r

The constant r1 is the unit vector associated with vector r and scalar r. This makes any dimensional analysis work out nicely.

 

[Gary A]

The Scientific Method and Quintessence

The Hyperbolic Field, Dark Matter and MOND​

Many workers have verified the fact that General Relativity does indeed regard black holes as both physical and logical or mathematical singularities, which means that they are point masses having infinite density and infinitely deep gravitational wells. This means they have an asymptotic (to both the abscissa and ordinate) gravitational potential profile. As such, their overall physical geometry must be consistent with their nature as singularities, or else the term "singularity" has no meaning. Their actual gravitational potential profile must be represented by a hyperbola.

The Scientific Method and Quintessence​

The scientific method requires scientists and all others who claim to think rationally to answer knotty questions by means of experiment (or careful observation). In order to do this effectively, one must formulate a hypothesis, a statement of the putative principle that engages all the known implications. These implications must be rather direct. Circumstantial consequences are just that - circumstantial and cannot PROVE a hypothesis. Those better former implications must suggest experiments that will verify them or not. It is good if there are direct elements of principle and subservient implications of the hypothesis. It is better if a complete and utter negative statement of the hypothesis can be formulated. Then, the net sum of the original hypothesis and the negative hypothesis should be zero. Logically, the negative completely cancels the positive hypothesis. This negative hypothesis is called the "null" hypothesis because it would nullify the other if it proves to be true and it would tend to validate the positive hypothesis, at least it would fail to PROVE it false, if it was shown to be false in any way. Then, if direct evidence can be found that tends to corroborate the original positive hypothesis, we can begin to regard it as a good logical beginning. THEN, if this positive hypothesis can be combined with statements that have already been proven and the combined implications can be verified, we have the beginnings of proof.

The key to this process is our ability to form an experimentally testable Null Hypothesis. The evidence FOR the positive statement of the hypothesis is insufficient in itself because circumstances may combine to fool our little experiments. We are human. If an appropriate robust Null Hypothesis cannot be formulated, the original hypothesis is unsuitable to merit the attention of the scientist.

This is relevant to the debates about Dark Energy, quintessence and Dark Matter. Dark energy is the reservoir of potential energy that is supposed to exist as an underlayment or foundation of the universe. Quintessence is supposed to be a new force field that is just another component of the universe. All fundamental force fields have an associated particle. So, if there is quintessence, there should be a quintessence particle also. Invisible Dark Matter is supposed to account for the anomalous rotation velocity distribution seen in galaxies and galactic clusters.

To call one's self a scientist, one must respect the scientific method. It is not a scientist's dogma any more than is it such to follow a firefighter's code; one must respect the power of fire - or else you die.

An unfalsifiable hypothesis has no business occupying the time of the scientist. Whole theories have often been constructed from unfalsifiable hypotheses. Such theories are often fun to think about, even edifying and inspiring - but they certainly are not science.

There is a place for faith. But, if a person of faith needs experimental proof, he will have little of either. We all need faith. We all use faith in some way. In times of trouble and sorrow, sometimes it is all we have. God loves us, we believe. Our belief makes it so. If we can say sincerely that a principle of human conduct or relations should be true, then it is. Human reality is what we can say it should be. This is called Primary Christian Existentialism. All men and women of faith are Christian existentialists.

All scientists hew to a code of honor as well as to the scientific method. Truth is not just a buzzword. Truth is meaning. Truth is the scientist's life. Truth is noble.

In a very real sense, to the scientist, "Truth" is the next best thing to God.

 

[Gary A]

No Trouble with Tribbles

No Trouble with Tribbles​

There is no trouble with Birkhoff’s Theorem which says: All gravity fields (including BHs’) act like normal Newtonian fields because all gravity fields drop out of GR naturally and so must be “asymptotically flat”, that is, they must vanish at large distances, i.e. they must follow an inverse square law.

BUT, Birkhoff is based on the particulars of the massive bodies that are treated, like stars, such particulars as the metric are used as a premise. The theorem says any spherically symmetric field must be asymptotically flat because any mass already behaves as if all its mass was concentrated at the center. It already behaves like a point mass. So, Birkhoff should rule out the hyperbolic (1/kr) supermassive Black-Hole singular galactic gravitational field.

Yet, none of the BH scenarios that are theoretically covered can be considered real. All real BHs are perturbed beyond recognition by their immense quantities of environmental matter and energy, including enormous external gravity fields. Such fields emanate from huge galactic disks or from other whole galaxies with their own embedded supermassive BHs.

Real conditions should invalidate the theorem.

One critical consideration is that black-holes are not mere point masses. They have been shown by Kretschmann and Schwartzchild to be physically real as infinitely dense particles with an infinitely deep gravitational potential well (within Heisenberg limits). They are NOT like a planet or a star. This is not properly reflected in the metrics with their singularities necessarily excluded, and is not adequately treated by Birkhoff or else it represents an exception. This observation may indicate a flaw or shortcoming in the way that general relativity is interpreted for spacetimes in the vicinity of black-holes, particularly near the singularity at r = 0.

Birkhoff used the Schwartzchild Metric. But, he could not rightly use the existence of an infinitely deep gravitational well or an infinitely dense point particle because these singular infinities cannot be handled normally. “The physics at a singularity is not well defined.”

It is far easier to accept the possibility of a flaw or exception than to accept the idea of some sort of unfalsifiable Dark Matter comprised of, say, undetectable WIMPs (weakly interacting massive particles). By their very nature WIMPs are supposed to be so “weakly interacting” that they cannot even show up in particle accelerator experiments. The WIMP hypothesis is formulated to be as unfalsifiable as any of the other Dark Matter proposals. As such, it does not merit the label “science”. It is more like science fiction.

So, an hyperbolic (F = GMm/kr) supermassive BH galactic gravity field is possible after all: k = constant = 1m (S.I.), for dimensional integrity. Einstein referred to his equations as being hyperbolic/elliptical in nature. That is, hyperbolic geometry is not outside the realm of GR.

Kretschmann’s invariance and Schwartzchild’s analysis mean that the singularity at the core of a BH is physically real. From our external frame of reference, the exact location of a BH singularity cannot be found because of the Heisenberg limit. So, from our external perspective, a BH core density and central gravity strength cannot be directly “measured” to be “infinite”. But, mathematically, it is so. And, elementary analytic geometry says that an infinitely deep graphical gravity potential growing from an hugely heavy infinitely dense point mass MUST be asymptotic in nature (NOT asymptotically flat). By symmetry, the other arm of the graphical curve must be asymptotic too, the definition of a hyperbola.

If you can collaborate on a paper, let us prove that an hyperbolic spacetime geometry around a realistic supermassive black-hole can be real and that the (1/kr) field can, indeed, account for all effects currently ascribed to so-called “Dark Matter”. As a partner, of course, I shall do a yeoman’s share of work, including the scut-work of referencing & literature search. I am in an ideal position to do this!

garyakent@aol.com

 

[AlphaNumeric]

It is far easier to accept the possibility of a flaw or exception than to accept the idea of some sort of unfalsifiable Dark Matter comprised of, say, undetectable WIMPs (weakly interacting massive particles). By their very nature WIMPs are supposed to be so “weakly interacting” that they cannot even show up in particle accelerator experiments. The WIMP hypothesis is formulated to be as unfalsifiable as any of the other Dark Matter proposals. As such, it does not merit the label “science”. It is more like science fiction.

Firstly weakly interacting particles can be detected by detectors, we see neutrinos regularly so your claim it is not science is wrong. Secondly it wasn't formulated to be unfalsifiable, that's just dishonest. Third dark matter has nothing to do with Birkhoff's theorem and it too is not unfalsifiable and has considerable evidence.

If your ideas have merit you shouldn't have to lie.

So, an hyperbolic (F = GMm/kr) supermassive BH galactic gravity field is possible after all: k = constant = 1m (S.I.), for dimensional integrity.

You haven't shown they are possible, you haven't shown a flaw in the theorem. As the theorem highlights, it doesn't actually matter how the mass inside a spherical region is distributed. If it's arranged as a shell rather than a point you get the same external metric but without the internal singularity. That's the whole point, when you get far enough away you don't care whether there's a singularity or not because how the matter is distributed radially isn't important.

Einstein referred to his equations as being hyperbolic/elliptical in nature. That is, hyperbolic geometry is not outside the realm of GR.

You're misunderstanding the term. Partial differential equations, which the field equations are, are classified as elliptic, hyperbolic or parabolic depending upon a particular sign structure in the derivatives. For example, the Laplacian is elliptic but the d'Alembert operator is hyperbolic. It's much like the signature of a metric (in the case of those operators literally). It doesn't mean the geometry is elliptical or hyperbolic.

If you can collaborate on a paper, let us prove that an hyperbolic spacetime geometry around a realistic supermassive black-hole can be real and that the (1/kr) field can, indeed, account for all effects currently ascribed to so-called “Dark Matter”. As a partner, of course, I shall do a yeoman’s share of work, including the scut-work of referencing & literature search. I am in an ideal position to do this!

I fail to see why anyone versed in general relativity sufficiently well to be capable of writing papers would want to work with you. Why are you in an 'ideal position'? Are you an academic? Unlikely, else you'd not be using an AoL email and asking for collaborators on forums. You'd also not be presenting your 'work' here, you'd be writing your own papers.

Concepts like having black hole solutions where the large distance limit is not Euclidean space but AdS (ie hyperbolic geometry) space are not new concepts, they are already well studied. Results like the positive energy theorem have been proven for such systems. I distinctly remember being taught how to draw recursive Penrose diagrams for such space-time when I was a student.

So please explain why you're someone with collaborating with (just to be clear I don't wish to collaborate with you, I want to see why you think anyone at all in academia would).

 

[Gary A]

There have been misstatements and misinterpretations of Birkhoff’s Theorem

Firstly weakly interacting particles can be detected by detectors, we see neutrinos regularly so your claim it is not science is wrong. Secondly it wasn't formulated to be unfalsifiable, that's just dishonest. Third dark matter has nothing to do with Birkhoff's theorem and it too is not unfalsifiable and has considerable evidence.

If your ideas have merit you shouldn't have to lie.

The hypothesized detection limits for WIMPS, MACHOs and axions is adjusted downward after every experiment fails to detect them so that now, the detection limit is below any practical experimental technique. In other words, one cannot prove unequivocally that a statistically positive result is just due to noise or random events in the detector because if there is a signal, it is too weak to rise above the noise level.

So, even if the idea of WIMPS originally wasn't deliberately invoked to be unfalsifiable, the continual ad hoc re-adjustment of the hypothesis is, in fact, deliberate. The concept has actually evolved into an unfalsifiable hypothesis

You haven't shown they are possible, you haven't shown a flaw in the theorem. As the theorem highlights, it doesn't actually matter how the mass inside a spherical region is distributed. If it's arranged as a shell rather than a point you get the same external metric but without the internal singularity. That's the whole point, when you get far enough away you don't care whether there's a singularity or not because how the matter is distributed radially isn't important.

There have been misstatements and misinterpretations of Birkhoff’s Theorem. For instance, it has been shown by Kristin Schleich and Donald M. Witt (“A simple proof of Birkhoff's theorem for cosmological constant”, arXiv: 09084110v2, 27oc09) that Birkhoff does not demand staticity in spherically symmetric solutions to Einstein’s vacuum field equations. Static solutions have heretofore been thought of as being required. There may be other misstatements and misinterpretations that are not yet recognized.

I do not quibble with Birkhoff. This would be a fatuous waste of time. I have issues with bad interpretations and misstatements of its meaning. For instance, Birkhoff’s Theorem must actually leave black hole singular gravitational fields as an exception to the commonly quoted rigid rule that only asymptotically flat (commonly assumed meaning: inverse square) gravitational fields are allowed. Otherwise there is no way to measure or unequivocally determine (or not) that the center of a black hole is a singularity since electric charge and gravity are the only items the influence of which can escape the interior of a black hole. Then the theories of Schwarzschild and Kretschmann that say such singularities are physically real are themselves largely meaningless as unfalsifiable hypotheses.

There simply must be a measurable consequence of a true singularity at the center of a black hole or else its existence cannot even be postulated. That the mathematics seems so very precise is not good enough. There must always be a way to experimentally verify or falsify the equations.

If the gravitational singularity at the center of a super-massive galactic black hole results in a hyperbolic gravitational field, there is a way. By measuring the velocity distribution of stars in the surrounding galactic disk, it can be determined if they move with a constant velocity, v = (GM)^½ at large r, as they must if they move in a hyperbolic gravitational field. As a matter of fact, the velocities of stars in spiral galaxies do indeed move with constant velocity at large r. This can be seen as proof of a singularity at the center of a spiral galaxy’s black hole. Wouldn't this be a really good thing?

We often state that “The laws of physics must break down at the incredibly tight curvature of spacetime near the singularity of a black hole”. What does this mean? One thing it could mean is that Birkhoff’s Theorem breaks down too. The metrics to which Birkhoff applies probably are not strictly valid near the singularities that they themselves predict so, the “asymptotically flat” dictum may not be strictly true either. Otherwise, our cautionary statement is meaningless.

OR, do you say that there is indeed a theory that subsumes the tiny curvature near a black hole singularity? AND, what does this theory say about the hyperbolic field concept?

Besides, the intense benefit brought by the postulate of a hyperbolic galactic super-massive black hole gravitational field is too great to be ignored. It explains the anomalous stellar velocity distributions in galaxies, anomalous velocity distributions in galactic clusters, galactic lensing phenomena, temperature distributions within galaxies, Bullet Cluster type apparent offsets in the barycenters of colliding galaxy clusters, etc. It does everything that Dark Matter is supposed to do! So, Dark Matter is an unnecessary complication that violates Occam’s Rule.

I would much rather entertain the idea of the hyperbolic field than to allow the consequences of these other hypotheses. They all have very serious drawbacks and would require rewrites of more than one "standard model".

You're misunderstanding the term. Partial differential equations, which the field equations are, are classified as elliptic, hyperbolic or parabolic depending upon a particular sign structure in the derivatives. For example, the Laplacian is elliptic but the d'Alembert operator is hyperbolic. It's much like the signature of a metric (in the case of those operators literally). It doesn't mean the geometry is elliptical or hyperbolic.

I fail to see why anyone versed in general relativity sufficiently well to be capable of writing papers would want to work with you. Why are you in an 'ideal position'? Are you an academic? Unlikely, else you'd not be using an AoL email and asking for collaborators on forums. You'd also not be presenting your 'work' here, you'd be writing your own papers.

Concepts like having black hole solutions where the large distance limit is not Euclidean space but AdS (ie hyperbolic geometry) space are not new concepts, they are already well studied. Results like the positive energy theorem have been proven for such systems. I distinctly remember being taught how to draw recursive Penrose diagrams for such space-time when I was a student.

So please explain why you're someone with collaborating with (just to be clear I don't wish to collaborate with you, I want to see why you think anyone at all in academia would).

I think I have already stated that the idea of the hyperbolic field is not mine. Michael Rowan-Robinson mentioned it in a paper he wrote some time after the acceleration papers were published. Thank you for clues to additional references.

I only respond to some claims that some have made that general relativity cannot handle hyperbolic forms. You exactly pinpoint how it most certainly can. GR has been pretty thoroughly recast in terms of differential geometry. So the claim that I misstate that GR should be able to handle hyperbolic geometry because the issues that I refer to are not geometrical issues is disingenuous at best.

I am in an ideal position to collaborate because my small business runs itself, almost, so I can devote as much time to this project as it may need.

A collaborator should be interested because there are issues raised here that are momentous in their scope and importance. "The intense benefit brought by the postulate of a hyperbolic galactic super-massive black hole gravitational field is too great to be ignored." I am not the best collaborator that this other person could ask for. I am the only one.

Cosmologists will not like this idea. The LCDM model would have to be drastically revised. The consensus would have to change. There would have to be a paradigm shift. Since journal editors and referees endorse only papers that conform to the consensus (they would have been comfortable with the Pope’s decision to censor Galileo), no-one will publish a paper that challenges the commonly accepted interpretation of Birkhoff’s Theorem (which is intensely relevant).

So, Birkhoff's Theorem does too refer to this issue. However, by its own definitions, it does not apply to real BHs. Real BHs are massively perturbed to the point that we cannot portray these as mere "perturbations". They are influenced by perfectly coaxial concurrent galactic disks that are thousands of times more massive and can be expected to strongly change the shape of the gravity well in which BHs exist so that strong hyperbolic effects can propagate radially after all, because this propagation is externally assisted. Some supermassive BHs are influenced by other BHs as in galactic clusters wherein the gravitational influence would be strongly asymmetric, spherical symmetry being another prerequisite of Birkhoff's Theorem. Even the field of a galactic disk is not spherically symmetric or even radially symmetric.

Einstein wrote an addendum to one of his books entitled "The Non-symmetric Field". Maybe the relevant theorems and spacetime metrics could be reformulated with this in mind. This is why I need a collaborator.

And, if Birkhoff does break down in the vicinity of a gravitational singularity, how can this ever be proven? One would have to develop a whole new physics of the ultra strong curvature near black hole singularities. Unless it also had consequences outside the black hole, such a theory itself could not be falsified so, it could not be admitted as a part of science.

Catch 22 says "Anyone who wants to get out of combat duty isn't really crazy." Hence, pilots who request a mental fitness evaluation are sane, and therefore must fly in combat. I am not naive. We would be better off flying in combat duty than trying to fly the hyperbolic super-massive galactic gravitational field and its consequence to Dark Matter into some journal’s pages.

This is the real reason why I probably will never find a collaborator! It is also why I need one.

You are right. If I had any chance of actually publishing, I would not be writing for physics forums. But, the forums would be rather sparse if everyone refrained for this reason.

Still, I might actually find a collaborator with the necessary ability and connections. I am searching in other ways too.

 

[AlphaNumeric]

The hypothesized detection limits for WIMPS, MACHOs and axions is adjusted downward after every experiment fails to detect them so that now, the detection limit is below any practical experimental technique.

And then technology improves. 100 years ago we couldn't do measurements accurate enough to detect weak bosons and neutrinos, now we can.

In other words, one cannot prove unequivocally that a statistically positive result is just due to noise or random events in the detector because if there is a signal, it is too weak to rise above the noise level.

Which is why a particle isn't considered to be 'discovered' until the data is such that it's less than a 1 in a million shot of being random noise (ie a 5 sigma deviation).

So, even if the idea of WIMPS originally wasn't deliberately invoked to be unfalsifiable, the continual ad hoc re-adjustment of the hypothesis is, in fact, deliberate. The concept has actually evolved into an unfalsifiable hypothesis

It's a possibility that they exist, along with many other things, and so people compute what sort of signature they would give in detectors. It's how we found the W and Z bosons of electroweak theory, they were predicted before they were observed and the manner of observation drove the design of experiments.

There have been misstatements and misinterpretations of Birkhoff’s Theorem. For instance, it has been shown by Kristin Schleich and Donald M. Witt (“A simple proof of Birkhoff's theorem for cosmological constant”, arXiv: 09084110v2, 27oc09) that Birkhoff does not demand staticity in spherically symmetric solutions to Einstein’s vacuum field equations. Static solutions have heretofore been thought of as being required. There may be other misstatements and misinterpretations that are not yet recognized.

The inclusion of a cosmological constant alters things.

The equation when you include the cosmological constant is $$R_{ab} = \lambda g_{ab}$$, what is known as an Einstein manifold equation. Obviously you get the usual $$R_{ab}=0$$ if $$\lambda = 0$$. If you include a cosmological constant then you can get time dependency in things. The $$\lambda$$ is the integration constant in the Einstein-Hilbert equations so you can still have $$T_{ab}=0$$ in this situation.

Traditionally people set $$\lambda = 0$$ when they refer to Birkhoff's theorem. You're quibbling about people's choice of phrase rather than some actual problem in GR.

I do not quibble with Birkhoff. This would be a fatuous waste of time. I have issues with bad interpretations and misstatements of its meaning. For instance, Birkhoff’s Theorem must actually leave black hole singular gravitational fields as an exception to the commonly quoted rigid rule that only asymptotically flat (commonly assumed meaning: inverse square) gravitational fields are allowed. Otherwise there is no way to measure or unequivocally determine (or not) that the center of a black hole is a singularity since electric charge and gravity are the only items the influence of which can escape the interior of a black hole. Then the theories of Schwarzschild and Kretschmann that say such singularities are physically real are themselves largely meaningless as unfalsifiable hypotheses.

You are quibbling. You're saying that because the single point at the centre of a black hole is a singularity where the equations break down then the large distance properties are called into question. If anything Birkhoff's theorem shows the opposite, that you don't care what is in the middle.

To quote one of my old GR lecturers, GR is one of the few, if not only, theories in physics which predicts its own demise. It's physically valid in vast numbers of domains but it predicts singularities, where its description stops working. Pretty much every relativist thinks that there's a quantum gravity phenomenon going on which sorts all that out and GR is just the effective theory of that. For example, string theory has GR being the effective theory of quantum gravity and it can do all the black hole stuff on a quantum scale, such as getting the value for a black hole's entropy by considering the combinatorics of string microstates. Anything more than a few Planck lengths from the black hole's centre will be accurately described by general relativity and since Birkhoff's theorem is about the very large distance properties it's not bothered by the issue with singularities.

There simply must be a measurable consequence of a true singularity at the center of a black hole or else its existence cannot even be postulated.

As I said, you're talking about things whose true description will be in quantum gravity, not general relativity so few people think GR's take on them is exact, down to the sub-Planck scale.

GR is an effective theory, which is technical phrasing for it being an approximation to something more fundamental, in much the same way that electromagnetism is an effective theory for quantum electrodynamics or Newtonian mechanics is for relativistic mechanics. Putting too much stock in what GR says in a domain it isn't applicable to is asking for problems. If you ask Newtonian mechanics the electrons fired out from the old cathode ray tubes in TVs would be going faster than light, which we know they do not. Doesn't mean Newtonian physics was unscientific.

That the mathematics seems so very precise is not good enough. There must always be a way to experimentally verify or falsify the equations.

And we do test it to the limits of our abilities. To use a simpler example, electromagnetism says the electron is a point. It's self energy is infinite as a result. Is electromagnetism unscientific? We can't ever prove an electron is a point, we can only put upper bounds on its size. We can't ever prove the photon is massless, we can only put upper bounds on its mass. We can only work out implications if our predictions are wrong and look for those implications in experiments. If the photon has mass then charge isn't conserved for example.

If the gravitational singularity at the center of a super-massive galactic black hole results in a hyperbolic gravitational field, there is a way.

Except that, as Birkhoff's theorem shows, the far field gravitational properties of such a system are blind to whether the black hole's core is a point or a blob.

By measuring the velocity distribution of stars in the surrounding galactic disk, it can be determined if they move with a constant velocity, v = (GM)^½ at large r, as they must if they move in a hyperbolic gravitational field. As a matter of fact, the velocities of stars in spiral galaxies do indeed move with constant velocity at large r. This can be seen as proof of a singularity at the center of a spiral galaxy’s black hole. Wouldn't this be a really good thing?

Except it isn't a test for the singular or not nature of the black hole core.

We often state that “The laws of physics must break down at the incredibly tight curvature of spacetime near the singularity of a black hole”. What does this mean? One thing it could mean is that Birkhoff’s Theorem breaks down too.

No, it doesn't. It means that if you ask "What is the gravitational field within 0.1 Planck lengths of the centre of the black hole?" then you'll need to include quantum gravity in your description. Once you're far enough away (like $$10^{-25}$$ metres) you don't need to include quantum gravity effects, they don't work over such distances. At such distances you can use normal GR and get a very accurate answer. The further away, the more accurate GR becomes, just like if you go far enough away you can eventually start using Newtonian mechanics.

To use that example again, if everything is moving slowly and far apart from one another you can model gravitational processes using Newtonian gravity. However, if things get close to one another and move quickly, such as the motion of Mercury around our Sun, then the Newtonian gravity equations begin to break down, they are not accurate, as is seen by Mercury's precession. Birkhoff's theorem makes statements about distant properties, which is precisely where GR is valid.

The metrics to which Birkhoff applies probably are not strictly valid near the singularities that they themselves predict so, the “asymptotically flat” dictum may not be strictly true either.

Do you even know what 'asymptotically flat' means? It means far away the space-time tends towards the flat metric. Far away, where GR is valid and its equations don't break down.

OR, do you say that there is indeed a theory that subsumes the tiny curvature near a black hole singularity? AND, what does this theory say about the hyperbolic field concept?

Such a theory would be quantum gravity and since it has to predict gravity's properties are large distances accurately and we know GR does that quantum gravity would have to have GR as an effective theory. It's one of the reasons many people work on string theory, it includes gravity quanta and they behave like GR says they should when you take their effective theory.

Besides, the intense benefit brought by the postulate of a hyperbolic galactic super-massive black hole gravitational field is too great to be ignored.

I haven't seen any yet.

It explains the anomalous stellar velocity distributions in galaxies, anomalous velocity distributions in galactic clusters, galactic lensing phenomena, temperature distributions within galaxies, Bullet Cluster type apparent offsets in the barycenters of colliding galaxy clusters, etc. It does everything that Dark Matter is supposed to do! So, Dark Matter is an unnecessary complication that violates Occam’s Rule.

When you can demonstrate any of that in a manner more than arm waving maybe people will listen.

I only respond to some claims that some have made that general relativity cannot handle hyperbolic forms.

GR has been pretty thoroughly recast in terms of differential geometry. So the claim that I misstate that GR should be able to handle hyperbolic geometry because the issues that I refer to are not geometrical issues is disingenuous at best.

I'm not entirely sure you understand that 'hyperbolic' can mean different things in different situations. An partial differential equation is called hyperbolic if its principle symbol can vanish in a particular way, ie it takes on the form of a hyperbolic function. That doesn't necessarily mean the solutions to the equation will have the form of hyperbolic functions. The wave operator $$-\partial_{t}^{2} + \Delta$$ is hyperbolic but its solutions are not necessarily hyperbolic.

I am in an ideal position to collaborate because my small business runs itself, almost, so I can devote as much time to this project as it may need.

Academics are paid to do research day in, day out, so it's not like having time to devote to something makes you ideal or unique. If you don't know much GR or differential geometry or partial differential equations then you're in a less than ideal situation. There's more to doing science than just having time on your hands.

A collaborator should be interested because there are issues raised here that are momentous in their scope and importance. "The intense benefit brought by the postulate of a hyperbolic galactic super-massive black hole gravitational field is too great to be ignored." I am not the best collaborator that this other person could ask for. I am the only one.

Cosmologists will not like this idea. The LCDM model would have to be drastically revised. The consensus would have to change. There would have to be a paradigm shift. Since journal editors and referees endorse only papers that conform to the consensus (they would have been comfortable with the Pope’s decision to censor Galileo), no-one will publish a paper that challenges the commonly accepted interpretation of Birkhoff’s Theorem (which is intensely relevant).

So, Birkhoff's Theorem does too refer to this issue. However, by its own definitions, it does not apply to real BHs. Real BHs are massively perturbed to the point that we cannot portray these as mere "perturbations". They are influenced by perfectly coaxial concurrent galactic disks that are thousands of times more massive and can be expected to strongly change the shape of the gravity well in which BHs exist so that strong hyperbolic effects can propagate radially after all, because this propagation is externally assisted. Some supermassive BHs are influenced by other BHs as in galactic clusters wherein the gravitational influence would be strongly asymmetric, spherical symmetry being another prerequisite of Birkhoff's Theorem. Even the field of a galactic disk is not spherically symmetric or even radially symmetric.

Einstein wrote an addendum to one of his books entitled "The Non-symmetric Field". Maybe the relevant theorems and spacetime metrics could be reformulated with this in mind. This is why I need a collaborator.

And, if Birkhoff does break down in the vicinity of a gravitational singularity, how can this ever be proven? One would have to develop a whole new physics of the ultra strong curvature near black hole singularities. Unless it also had consequences outside the black hole, such a theory itself could not be falsified so, it could not be admitted as a part of science.

Catch 22 says "Anyone who wants to get out of combat duty isn't really crazy." Hence, pilots who request a mental fitness evaluation are sane, and therefore must fly in combat. I am not naive. We would be better off flying in combat duty than trying to fly the hyperbolic super-massive galactic gravitational field and its consequence to Dark Matter into some journal’s pages.

This is the real reason why I probably will never find a collaborator! It is also why I need one.

You are right. If I had any chance of actually publishing, I would not be writing for physics forums. But, the forums would be rather sparse if everyone refrained for this reason.

Still, I might actually find a collaborator with the necessary ability and connections. I am searching in other ways too.

Now I see you're just a loopy hack.....