Can Anyone Answer These Black Hole Problems?

[A-wal]

1. When an object approaches an event horizon it approaches at an ever decreasing rate the closer it gets from the perspective of a more distant observer because of length contraction and time dilation. It can never reach the event horizon because the rate that length contracts and time dilates from the perspective of a distant observer is identical to the rate that length contracts and time dilates from the perspective of an inertial object observing an accelerating object approaching the speed of light because approaching an event horizon and approaching the speed of light are the same thing. The only difference is that the object is being accelerated by mass (gravity) instead of being accelerated by energy. The Schwarzschild coordinate system also describes an object using energy to accelerate. Free-fall is not inertial! If an object were able to reach an event horizon it would be travelling at the speed of light relative to the singularity, and every external object. If an object can never reach an event horizon from the perspective of any external object then it's always possible for the object to accelerate away. It's never too late from the perspective of any external object so it can never be too late from the perspective of a falling object. This is a definite yes/no situation that cannot be Lorenzed away!

Three ships approach a 'black hole'. One ship continuously accelerates at a constant rate to keep itself stationary relative to the 'black hole'. One ship cuts off its engines and free-falls. The last ship accelerates away from the hovering ship and steadily increases its acceleration at an ever increasing rate so that it's always moving away from the hovering ship at exactly the same speed as the the free-falling ship is in the opposite direction. From the perspective of the hovering ship the other two ships are continuously becoming more length contracted and time dilated to keep their relative velocities below the speed of light. According to the standard description if we then switch to the perspective of the ship that's accelerating away from the black hole there's no contradiction between the two frames of reference, which is right. This is special relativity. Now if we switch to the perspective of the free-falling ship then according to the standard description it's perfectly okay for the free-falling ship to reach and cross the event horizon despite the fact that it can never happen from the other two ships, or any other objects perspective. This makes no sense! It's a direct contradiction. They have to use multiple coordinate systems to describe the whole thing. If you treat special and general relativity as equivalents of each other then you can use a single unified coordinate system that covers the entire manifold, which you should always be able to do. It's not okay to contradict yourself like this and then claim that it's a self consistent description of reality.

2. Black holes are described as having an event horizon that's expanding outwards at the speed of light locally (slower from a distance as an inverse square). Information propagates through space-time at the speed of light (again, slower as an inverse square of the distance from the 'black hole'), so how can the gravitational influence of the black hole reach any object before the event horizon does?

3. No object can ever be observed reaching an event horizon from the perspective of any external object because if that where possible then you could observe objects crossing the horizon as you approach it and they would have to then cross back from the inside if you accelerate away. If no object closer the the horizon can reach it before you do then all the objects that ever reach the horizon would have to do it at exactly the same time. Traffic jam!

4. If a free-falling object can cross an event horizon then what happens if it's attached by a rope to an object outside the horizon that then accelerates away? From the external objects perspective it's always possible to pull the other object away because it can never reach the horizon, but from the perspective of the object inside the horizon it can't be pulled away. Paradox!

5. A singularity is a singular point in time as well as space so it doesn't last for any length of time. Its length in time and space get extended by the same amount as the observers distance increases, making it appear to occupy more space-time the further away it's viewed from (again as an inverse square) making it a perfect four dimensional sphere (hypersphere). In the standard model it's cone shaped in four dimensions. Why would it be cone shaped when space and time are equivalent?

6. As you approach a 'black hole' it gets more length contracted and time dilated the closer you get because of the increased gravitation. If an object were able to reach the event horizon then it would be moving at the speed of light relative to the singularity, so the event horizon would be infinitely length contracted and time dilated. A 'black hole' is just what a singularity looks like from a distance!

7. When an objects accelerates using energy there's what's called a Rindler horizon behind it that gets closer to it if it increases its acceleration and further away from it if it decreases its acceleration. No information from beyond this horizon can ever catch up to the accelerating object as long as carries on accelerating at at least the same rate. It approaches at a slower rate in response to the same increase in acceleration the harder the object is accelerating, in exactly the same way that length contraction and time dilation make an objects relative velocity increase at slower rate response to the same amount of acceleration the faster its relative velocity to keep it below the speed of light. Acceleration can be defined as velocity relative to energy. This prevents an accelerating objects Rindler horizon from ever catching up to it, which wouldn't make sense. A Rindler horizon is always exactly the same distance away from the accelerating object as the horizon of it's own light moving away in front of it (the speed of light is only constant for inertial objects, it doesn't apply when they accelerate). There's also a Rindler horizon behind free-falling objects which works in exactly the same way. If an object were able to reach an event horizon then it's own Rindler horizon would have to catch up to it and overtake it so that it's the same distance in front of the object as the event horizon is behind it. It makes no sense for the two horizons to cross over like this. Instead the event horizon works in exactly the same way that the speed of light horizon does for an object using energy to accelerate, because it's the same thing. They're perfectly equivalent.

8. The laws of physics are supposed to be time reversible, but black holes as they're currently described clearly break this rule. If it were possible for an object to cross the event horizon of a black hole then if the arrow of time were reversed then that object would have to reemerge from inside the event horizon despite the fact that gravity is an attractive force regardless of the direction of the arrow of time, which is supposed to be impossible. This is just one more example that shows that black holes as they described aren't even self consistent.

White holes are supposed to be the solution to a time reversed black hole but they make even less sense than the way black holes are described. They have no way to form for a start, and they repulse objects with infinite force. What force is that supposed to be? Gravity? It's always an attractive force. It's not a valid solution because objects being able to reach an event horizon isn't a valid solution. The Schwarzschild coordinate system clearly shows this. Try using Schwarzschild coordinates to describe a white hole. You'd obviously have to start with the objects outside the horizon. The only answer anyone seems to be able to give is that Schwarzschild coordinates aren't valid when an object reaches an event horizon. What does that even mean? How close does an object have to be before that coordinate system becomes invalid? It can't be at the horizon because objects can't reach an event horizon using Schwarzschild coordinates. The Rindler coordinate system is another valid system that can be applied to objects being accelerated by gravity as well as energy, and again the event horizon is unreachable. A time reversed black hole is still a black hole.


Instead of treating acceleration due to energy (special relativity) as a special case within the generalised structure of gravitationally curved space-time (general relativity), they should be put on an equal footing. If you do this, something truly amazing happens. They become two sides of the same acceleration coin. Gravity is considered an inward curvature of space-time, pulling objects together, but you can just as easily view energy as an outward curvature of space-time, pushing objects apart. There is absolutely no difference between following a straight line in curved space-time and following a curved path in flat space-time. They're physically equivalent. Tomato, tomato. That was just a very brief outline. I'm in the process of writing it up properly. In the mean time:

I don't believe in the big bang. The universe is curved, just like the Earth. When looking across a curved surface objects don't just disappear out of view all of a sudden. The light gets stretched making it redshifted and the further away the object is the more redshifted it is because there's obviously more curvature the greater the distance, which explains exactly way objects tend to be more redshifted the further away the are. The universe is spherical. This doesn't mean that it has edges/borders though. It's not a three dimensional object, you have to think of a four dimensional sphere (hypersphere). Any point in space-time is at the centre of the sphere from its own perspective, with a horizon the same distance away in all directions. This also applies to time in exactly the same way. If we could live forever then we'd end up at exactly the same point of time that we started at. We wouldn't remember having been there before though because you can't get any information through a singularity (although that's not what it would look like if you were there).

In the standard model gravity rules. Special relativity describes acceleration due to energy and general relativity describes acceleration due to mass (gravity). In the standard model sr is put within the framework of gr as a kind of sub-theory, as a special case within a gravitational framework of curved space-time. I believe this was a huge mistake. There's absolutely no difference between following a straight path in curved space-time and following a curved path in flat space-time from a localised perspective. They're physically equivalent. If you reverse everything within a system then nothing changes. To see the change you need to view it from an external frame of reference.

It's not really that black holes don't exist as such. They are obviously intense bodies of gravitation that emit no light, that much is obvious, but calling them black holes isn't a generic statement. It's claiming that a very specific physical process is occurring that makes no sense mathematically or logically. There's a far simpler explanation based purely on special relativity. To put it simply general relativity claims that gravity is able to accelerate objects to a relative velocity faster than light despite the fact that length contraction and time dilation apply in the exact same way to gravitational acceleration as they do to acceleration caused by energy, which is backed up by the fact that no object can ever witness another object reaching an event horizon. They're described by mainstream cosmology in a very self contradictory way. Singularities do exist, sort of. They occupy a single point of space-time, they don't exist for any amount of time as well as being infinitely small in space. This is because they're infinitely time dilated and length contracted from their own frames of reference. As the distance between the black hole and the observer increases, the size of the black hole increases at a progressively slower rate the greater the distance (as an inverse square of the distance) because there's less time dilation and length contraction the further away they're observed from. This makes them perfect four dimensional spheres (hyperspheres). As an object approached an event horizon the dime dilation and length contraction increase, making the black hole progressively smaller. It's exactly the same as observing an acceleration object approaching the speed of light in special relativity. If an event horizon were reachable (completely impossible because it's the equivalent of accelerating to the speed of light and they don't exist for any length of time) then the black hole would be infinitely time dilated and length contracted, making it a singularity. A black hole is just what a singularity looks like from a distance/a singularity is what a black hole looks like from it's own frame of reference.

 

[AlphaNumeric]

Please please please make your posts less verbose. Opening a thread and the opening post being a wall of text is going to make people who might want to talk about black holes think "Sod that!" and go away. I'll give short answers to each question, rather than lengthy ones, because otherwise discussion will be impossible. I suggest you pick a particular answer I give and we go from there.

My first comment is that they are not 'perfect 4 dimensional spheres'.

1. Your description is wrong. If A and B start far from the black hole, holding at a constant distance using engines and then B begins falling towards it then from A's point of view B will never reach the event horizon. However, from B's point of view he will cross the event horizon in finite time and hit the singularity in finite time. So your comment that it is never too late to turn around is wrong. Suppose B has a watch on and at 12 noon begins falling towards the black hole. A can see the watch on B's wrist and if B saw 1pm on his watch when he crosses the event horizon then it means A will never see B's watch get to 1pm. Your description makes it seem like you think there's some universal notion of time and if A never sees B get to the point of no return then B has just as much time to escape. No, he doesn't. A measures infinite time, B measures finite. The derivation of this result is standard bookwork in any GR course.

2. Who describes a black hole as having an event horizon which expands out at the speed of light? And what does the inverse square law have to do with it? When a non-rotating uncharged black hole of mass M forms then the event horizon appears at the distance $$R = \frac{2GM}{c^{2}}$$ from the core. An object 1 metre above the event horizon will need to use engines to stop from falling in but the event horizon isn't moving towards it at any speed, never mind the speed of light. The event horizon's size is entirely determined by the mass via the expression I just gave. This generalises to include charge and angular momentum terms for the Kerr-Newman rotating charged black hole but those are the only 3 things it can depend on (in 3+1 dimensions anyway). This is the 'no hair theorem'.

3. The objects would seem to get bunched up yes but they never meet if they all feel at the same rate just at different times.

4. The rope snaps. Ropes and any other material are held together by the electromagnetic interactions between the atoms which make up the material. Light cannot escape the event horizon and thus there is no way for the rope already in the event horizon to communicate with the rope outside of the event horizon, in other words it is cut. Was your 'paradox!' exaltation sarcastic? I hope so because otherwise it suggests you honestly think you've found a paradox within a mathematically formalised physical model you have no working familiarity with and only the most passing of knowledge of on a qualitative level. Were you serious?

5. Your assertion is false. The singularity is local in space, not in time. This means in the 3+1 dimensional space-time it is contained within it sweeps out a 1 dimensional worldline. As would any other point object. 'Singularity' is not defined as zero dimensional in space and time. The Schwarzchild black hole solution is a zero dimensional point in space which sweeps out a 1 dimensional worldline. The charged spinning black hole solution by Kerr and Newman has a singularity which is not a point but a ring. It couldn't be a point because a zero dimensional object cannot carry any angular momentum. More complicated singularities exist when you consider 5 dimensional general relativity and even more complicated ones when you work with string theory. For example, in models trying to construct a gravity/gauge dual to QCD it is necessary to consider a 7 dimensional object stretched through a space-time whose geometry is defined by a stack of 3 dimensional 'black branes', ie singularities but they have 3 spatial dimensions, not the zero of the Schwarzchild black hole. 'Black branes' are of considerable interest to theoretical physics. You said it had zero time duration, which is false. Something which has zero time duration is referred to in the literature as an 'instanton', ie it exists only for an instant.

6. That isn't even a question. Now we're into the realms of you just giving us your extremely dubious opinion about a realm of physics you have no experience with and which is often extremely counter intuitive. Likewise with 7,8,9 so I'll just skip them.

Yes, we get it, you've just read some pop science book about black holes and now you want to tell everyone all the amazing knowledge you have. It's good you want to learn about these things, when I was 16-18 I too read all the pop science books in my local book store, but speaking as someone who has been on both sides of the fence (read lots of pop science but no knowledge of the actual models vs having knowledge of the actual models) I can tell you that pop science overviews do not bestow on you sufficient knowledge of the details to be able to start making assertions of the kind you are. As I've just explained, you've been wrong numerous times.

 

[przyk]

AlphaNumeric already largely addressed the OP. A couple of my own responses:

Instead of treating acceleration due to energy (special relativity) as a special case within the generalised structure of gravitationally curved space-time (general relativity), they should be put on an equal footing.

They already are. That's what the principle of general covariance is all about. In the context of general relativity, when you 'feel' a local gravitational field, such as the gravitational field you feel standing on Earth, you are accelerating (in the sense that your proper acceleration, which is a relativistic invariant, is nonzero).

(Incidentally, you don't accelerate due to "energy". That sounds like a misconception of highschool level physics. You accelerate due to the presence of a net force acting on you.)

1. When an object approaches an event horizon it approaches at an ever decreasing rate the closer it gets from the perspective of a more distant observer because of length contraction and time dilation. It can never reach the event horizon because the rate that length contracts and time dilates from the perspective of a distant observer is identical to the rate that length contracts and time dilates from the perspective of an inertial object observing an accelerating object approaching the speed of light because approaching an event horizon and approaching the speed of light are the same thing. The only difference is that the object is being accelerated by mass (gravity) instead of being accelerated by energy. The Schwarzschild coordinate system also describes an object using energy to accelerate. Free-fall is not inertial! If an object were able to reach an event horizon it would be travelling at the speed of light relative to the singularity, and every external object. If an object can never reach an event horizon from the perspective of any external object then it's always possible for the object to accelerate away. It's never too late from the perspective of any external object so it can never be too late from the perspective of a falling object. This is a definite yes/no situation that cannot be Lorenzed away!

AlphaNumeric already answered this. I'll just point out that I happen to have given an answer to a similar question [POST=2629283]here[/POST] based on the Kruskal coordinate chart (which makes things particularly easy to visualise in this case). Short answer: objects can reach the event horizon in finite proper time (i.e. from the perspective of the object itself) and objects become irretrievable in finite time from the perspective of an external observer (in the sense that the point where the object crosses the event horizon drops eventually drops out of an external observer's future light cone).

2. Black holes are described as having an event horizon that's expanding outwards at the speed of light locally (slower from a distance as an inverse square). Information propagates through space-time at the speed of light (again, slower as an inverse square of the distance from the 'black hole'), so how can the gravitational influence of the black hole reach any object before the event horizon does?

A short answer is that the entire black hole solution, including the surrounding gravitational field, is a solution to the Einstein field equation (which basically defines GR). So a cheap answer is that this is allowed because general relativity predicts it, and the EFE "explains" how it is possible.

That said, there's a more intuitive answer. Basically, as has been mentioned elsewhere, an outside observer never sees matter cross the event horizon of a black hole (i.e. the point where the matter crosses the event horizon never drops out of an outside observer's past light cone) and that is also true of the matter that originally collapsed to form the black hole in the first place. So one way to think about it is that the gravitational field you're feeling isn't "created" by the black hole itself but rather all the matter that ever fell into it, about which information can still be reaching you indefinitely (because you never see matter actually cross the event horizon).

General relativity also allows such a thing as an "eternal" black hole that isn't formed by matter collapse. In that case there's a different answer: it turns out that the Schwarzschild eternal black hole solution also requires the presence of a white hole in the causal past, which is sort of the opposite of a black hole (e.g. matter and light can't enter it and can only escape from it). So you can think of the gravitational field you feel around an eternal Schwarzschild black hole as being created by the corresponding white hole.

5. A singularity is a singular point in time as well as space so it doesn't last for any length of time. Its length in time and space get extended by the same amount as the observers distance increases, making it appear to occupy more space-time the further away it's viewed from (again as an inverse square) making it a perfect four dimensional sphere (hypersphere). In the standard model it's cone shaped in four dimensions. Why would it be cone shaped when space and time are equivalent?

This is completely wrong. Actually it's probably better to think of the singularity as a 'surface' at a specific time but extended in space, which is how it appears in Kruskal-like charts. The idea of the event horizon as a point in space comes from the original description of the black hole solution in Schwarzschild coordinates. The problem is that Schwarzschild coordinates are a bit pathologically defined. Specifically, the Schwarzshild time and radial coordinates blow up on the event horizon and actually reverse roles inside the black hole. Within the event horizon, r is actually a timelike coordinate and t is actually a spacelike coordinate.

8. The laws of physics are supposed to be time reversible

The laws of physics aren't "supposed" to be anything except what they are, and a theory that "breaks" an external principle is not an internal inconsistency. As it happens, all the laws of physics that we know about, including general relativity, are time-reversible at the fundamental level, but we don't observe physics to be time-reversible at the macroscopic level. In many common, everyday scenarios, the time-reversed version of a macroscopic process is obviously thermodynamically impossible, which means that it is technically theoretically possible but extremely unlikely.

White holes are supposed to be the solution to a time reverses black hole but they make even less sense than the way black holes are described. They have no way to form for a start

I don't think you're thinking this through very carefully. White holes don't necessarily need to start. In classical physics, matter can't escape a black hole so a black hole that has formed simply continues to exist forever. The time-reversed version of that is a white hole that has simply always existed in the past, until all the matter constituting its mass escapes it.

Quantum field theory implies that black holes should eventually evaporate via Hawking radiation. The final stages of that evaporation aren't well understood with current physics (because we're getting into regimes where we need a theory of quantum gravity, which we don't have), but if you go with that and assuming the process is time-reversible, then you can imagine you could have white holes forming via some (probably extremely unlikely, but theoretically possible) process of "reverse Hawking radiation".

and they repulse objects with infinite force.

Who told you that? White holes don't actually repulse objects. It's just that their causal structure only allows one way travel out of the event horizon, just like the causal structure of a black hole only allows one way travel in. If you think of a black hole event horizon as expanding outward at the speed of light, then a white hole is the opposite of that. Just like with black holes, no actual "force" is involved.

 

[tashja]

Hi, A-Wal. More info if you need it. Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the ergosphere. The oval-shaped surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process).

Rotating black holes share many of the features of non-rotating black holes - inability of light or anything else to escape from within their event horizons, accretion disks, etc. But general relativity predicts that rapid rotation of a large mass produces further distortions of space-time in addition to those which a non-rotating large mass produces, and these additional effects make rotating black holes strikingly different from non-rotating ones.

Ergosphere

A large, ultra-dense rotating mass creates an effect called frame-dragging, so that space-time is dragged around it in the direction of the rotation.

Rotating black holes have an ergosphere, a region bounded by:

on the outside, an oblate spheroid which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, space-time is dragged around at the speed of light.
on the inside, the outer event horizon.

Within the ergosphere space-time is dragged around faster than light - general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary as seen by an external observer) because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way the black hole will spin more slowly and may even stop spinning eventually.

Ring-shaped singularity

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness - but remember that quantum mechanics does not allow objects to have zero size in any dimension (their wavefunction must spread), so general relativity's prediction is only the best idea we have until someone devises a theory which combines general relativity and quantum mechanics.

Possibility of escaping from a rotating black hole

Kerr's solution for the equations of general relativity predicts that:

The properties of space-time between the two event horizons allow objects to move only towards the singularity.
But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.
Passing through the ring shaped singularity may allow entry to a negative gravity universe.

If this is true, rotating black holes could theoretically provide the wormholes which often appear in science fiction. Unfortunately, it is unlikely that the internal properties of a rotating black hole are exactly as described by Kerr's solutionand it is not currently known whether the actual properties of a rotating black hole would provide a similar escape route for an object via the inner event horizon.

Even if this escape route is possible, it is unlikely to be useful because a spacecraft which followed that path would probably be distorted beyond recognition by spaghettification.


Tracy Hall
Posted: Nov 20 2006, 11:43 PM

A singularity is any quantity which is infinitely large or small. A point singularity, such as that hidden by the event horizon of a non-spinning black hole, has zero (infinitely small) thickness in all three dimensions. A ring singularity, such as that hidden by the event horizon of a spinning black hole, does have non-zero length (or circumference) in one dimension, but is still infinitely small in two of three dimensions, like an ideal straight line.

Incidentally, McClintock is quoted as saying that a black hole is completely described by the two numbers (actually, a scalar and a vector) describing mass and spin, but it is my understanding that a black hole can also have a non-zero electrostatic charge, and thus it requires three quantities to completely describe it. Mass and spin all there are for practical purposes, though--I wouldn't expect a physically existing black hole to carry any measurable charge.

AlphaNumeric
Posted: Nov 21 2006, 12:24 AM

Yep, by the 'No Hair Theorem' black holes are fantastically bland when it comes to their describing variables, just M (mass), J (=aM, a angular velocity) and Q (charge). The dynamics of the space-time in and around them though is very complex for depending on so few considerations!

Tracy, you're right in that it's generally considered to have Q=0. Although the Kerr-Newman metric is the most general, if you actually want to do any computation, seeing Q=0 is a valid approximation and reduces the complexity of the equations significantly!

A HUGELY charged black hole such that |Q|=M (in G=h=c=k=1 units) or a fast spinning and charged black hole such that |M|^2 = a^2 + Q^2, then you have an 'extremal black hole' which actually strips away it's event horizon! These aren't considered physical for two reasons. Firstly, it would be a naked singularity and those are prohibited by the 'Cosmic Censorship Hypothesis' and secondly because any black hole which gets up a big charge will attract oppositely charged particles into it and so even out it's charge a bit. It's essentially self-limiting.

Extremal black holes tend to pop up in string or M theory a lot because they are particularly nice solutions to some things.

 

[Captain Kremmen]

@A-Wal
Threads need to be about one subject which can be simply stated in the thread title.
Not a rule, but good practise which leads to more focussed discussions.

I doubt many people will read all your OP (Opening Post).
It is too much like eating a whole horse.
I suggest that you make six posts rather than one.

 

[A-wal]

@A-Wal
Threads need to be about one subject which can be simply stated in the thread title.
Not a rule, but good practise which leads to more focussed discussions.

I doubt many people will read all your OP (Opening Post).
It is too much like eating a whole horse.
I suggest that you make six posts rather than one.

I didn't want to spam the forum. Also if I made a separate topic for each problem the conversations would overlap anyway and it would end up a mess. I know, I'll swap it round. It would be better with the problems at the top, then people can read my motivation after if they want to.

Thanks for the replies btw. I haven't got time to reply at the moment. I just had a quick scan. I'll do it this evening.

 

[Prof.Layman]

Why do I always tend to get the feeling that the universe is just sitting there snickering at us, knowing good and well that one day all of our atoms will be completely obliterated into a dark void of nothingness? I would be in much need for comfort in knowing that there would be some safty net there to stop us from actually going into a black hole and my future atoms will be safe. These kind of bed time stories can be freightning, please make the bad man go away. What is this safty net exactly and how does it work? I toss and turn at night thinking that even if my time does stop, I would see the rest of the lifetime of the universe flash by in an instant, giving me plenty of time to slip right in just before the big rip.

 

[Captain Kremmen]

There is a theory that if you fall into a black hole, all your information is preserved like a hologram on the surface.
Instant immortality.

Perhaps someone could answer me a question, really quickly, as I don't want to divert the thread.
Why is there a problem in quantum physics with information being destroyed?

 

[RJBeery]

There is a theory that if you fall into a black hole, all your information is preserved like a hologram on the surface.
Instant immortality.

In terms of information, the same thing happens when you are cremated so don't get too excited about the prospect.

Perhaps someone could answer me a question, really quickly, as I don't want to divert the thread.
Why is there a problem in quantum physics with information being destroyed?

Because information necessarily has a physical manifestation, so it would be equivalent to violating the conservation of energy.

 

[Prof.Layman]

There is a theory that if you fall into a black hole, all your information is preserved like a hologram on the surface.
Instant immortality.

Ya but for how long could you experience that really? If time has stopped then you would only be able to experience that for that one moment, right?

Perhaps someone could answer me a question, really quickly, as I don't want to divert the thread.
Why is there a problem in quantum physics with information being destroyed?

It comes from the laws of thermodynamics, nothing can be created or destroyed. Nothing lost, nothing gained but when something goes into a black hole it could never come out, so then they try to prevent it from violating this law. Since it is law it would have to be true in all cases or it wouldn't be a law.

 

[hansda]

Ya but for how long could you experience that really? If time has stopped then you would only be able to experience that for that one moment, right?

"Time has stopped" really does not mean that "time has stopped flowing" in that locality. "Time" will still flow in that locality from 'past to present to future' as in any other locality. It only means that, at that locality "only the local "clock has stopped" ticking".

 

[Prof.Layman]

"Time has stopped" really does not mean that "time has stopped flowing" in that locality. "Time" will still flow in that locality from 'past to present to future' as in any other locality. It only means that, at that locality "only the local "clock has stopped" ticking".

That is why I mentioned that one moment it is around the time you went to the horizon of the black hole, and then wouldn't the next moment then be the end of the universe itself? Time would appear to be stopped for you from an outside observer, but from an observer at the event horizon time would keep marching on. So then when does it march to the next moment if time has stopped for you for all outside observers? I have also read that an observer falling into a black hole would see time speed up outside of the black hole, he would not observe their time to also slow down because he is the one that is being affected and it wouldn't be like a case in SR like the twin paradox.

 

[hansda]

That is why I mentioned that one moment it is around the time you went to the horizon of the black hole, and then wouldn't the next moment then be the end of the universe itself? Time would appear to be stopped for you from an outside observer, but from an observer at the event horizon time would keep marching on. So then when does it march to the next moment if time has stopped for you for all outside observers? I have also read that an observer falling into a black hole would see time speed up outside of the black hole, he would not observe their time to also slow down because he is the one that is being affected and it wouldn't be like a case in SR like the twin paradox.

To keep it simple: "time will march" but "the clock will not march".

 

[Prof.Layman]

To keep it simple: "time will march" but "the clock will not march".

A little too simple for my taste, I don't see how the tick of a clock and time itself can be independent from each other.

 

[hansda]

A little too simple for my taste, I don't see how the tick of a clock and time itself can be independent from each other.

Einstein actually explained "time" in terms of "simultaneity". This "simultaneity" can not be observed in the Black-Hole.

 

[Prof.Layman]

Einstein actually explained "time" in terms of "simultaneity". This "simultaneity" can not be observed in the Black-Hole.

What does this buzz word have to do with this?

 

[Captain Kremmen]

It comes from the laws of thermodynamics, nothing can be created or destroyed. Nothing lost, nothing gained but when something goes into a black hole it could never come out, so then they try to prevent it from violating this law. Since it is law it would have to be true in all cases or it wouldn't be a law.

That's the law of Conservation of Energy.
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. The total energy of an isolated system remains the same.

Information is not Energy.
Why can information not be destroyed?

 

[A-wal]

Please please please make your posts less verbose. Opening a thread and the opening post being a wall of text is going to make people who might want to talk about black holes think "Sod that!" and go away. I'll give short answers to each question, rather than lengthy ones, because otherwise discussion will be impossible. I suggest you pick a particular answer I give and we go from there.

I read the forum rules and there's nothing about verbose posts.

My first comment is that they are not 'perfect 4 dimensional spheres'.

I know they're not according to general relativity. That's what I'm trying to refute.

1. Your description is wrong. If A and B start far from the black hole, holding at a constant distance using engines and then B begins falling towards it then from A's point of view B will never reach the event horizon. However, from B's point of view he will cross the event horizon in finite time and hit the singularity in finite time. So your comment that it is never too late to turn around is wrong. Suppose B has a watch on and at 12 noon begins falling towards the black hole. A can see the watch on B's wrist and if B saw 1pm on his watch when he crosses the event horizon then it means A will never see B's watch get to 1pm. Your description makes it seem like you think there's some universal notion of time and if A never sees B get to the point of no return then B has just as much time to escape. No, he doesn't. A measures infinite time, B measures finite. The derivation of this result is standard bookwork in any GR course.

I'm sure it is, but that's not the point. You're deflecting. Of course I'm not implying that there's a universal notion of time. It's very simple. What I'm saying is that it's never too late for a free-falling object to accelerate away from a black hole, so you could wait however long you want and that object will still always be able to move away, so it never reaches the event horizon. At no time in the black holes life can any object ever reach the event horizon from the perspective of an external object, so at no time in a black holes life can any object reach the event horizon, so at no time can any object reach an event horizon, so no objects can ever reaching a sodding event horizon!

2. Who describes a black hole as having an event horizon which expands out at the speed of light? And what does the inverse square law have to do with it? When a non-rotating uncharged black hole of mass M forms then the event horizon appears at the distance $$R = \frac{2GM}{c^{2}}$$ from the core. An object 1 metre above the event horizon will need to use engines to stop from falling in but the event horizon isn't moving towards it at any speed, never mind the speed of light. The event horizon's size is entirely determined by the mass via the expression I just gave. This generalises to include charge and angular momentum terms for the Kerr-Newman rotating charged black hole but those are the only 3 things it can depend on (in 3+1 dimensions anyway). This is the 'no hair theorem'.

I've heard black holes being described by more than one professional physicist as having event horizons that expand outwards at the speed of light locally. It seems from my experience that there isn't even a consensus amongst physicists about the physics of black holes.

3. The objects would seem to get bunched up yes but they never meet if they all feel at the same rate just at different times.

That doesn't work. Think about it. If no object can reach the event horizon in front of you then all the free-falling objects would have to meet at the event horizon.

4. The rope snaps. Ropes and any other material are held together by the electromagnetic interactions between the atoms which make up the material. Light cannot escape the event horizon and thus there is no way for the rope already in the event horizon to communicate with the rope outside of the event horizon, in other words it is cut. Was your 'paradox!' exaltation sarcastic? I hope so because otherwise it suggests you honestly think you've found a paradox within a mathematically formalised physical model you have no working familiarity with and only the most passing of knowledge of on a qualitative level. Were you serious?

Damn right I'm serious! You're saying that in moment it's possible for the free-falling object to escape and the next all the energy of a trillion universes isn't enough to accelerate away, but only from the free-falling objects perspective. This simply isn't remotely plausible. Besides, from the outside objects perspective it's always possible to pull out the other object with a finite strength rope because the closer object is always outside the horizon from the further objects perspective. Explain that. Don't deflect, just answer the question.

Ah now you see, if the rope has to snap then all objects get atomised as they reach the event horizon as same thing applies to any extended object because the front of it will have to rip away from the rest of it because if the rope has to snap then that's an infinite amount of energy (which is completely ridiculous btw) and the free-falling object doesn't need to be accelerating in the opposite direction for it to have to snap, and then the new front of the object will rip away from the rest of it, and so on. The rope isn't at all necessary, it's just to make it easier to visualise. You've just inadvertently asserted that the standard view that objects can cross the event horizon of a super massive black hole without being ripped to shreds is in fact completely false. I told you this was going to be fun, for me anyway. Are you having fun? I'm having fun.

5. Your assertion is false. The singularity is local in space, not in time. This means in the 3+1 dimensional space-time it is contained within it sweeps out a 1 dimensional worldline. As would any other point object. 'Singularity' is not defined as zero dimensional in space and time. The Schwarzchild black hole solution is a zero dimensional point in space which sweeps out a 1 dimensional worldline. The charged spinning black hole solution by Kerr and Newman has a singularity which is not a point but a ring. It couldn't be a point because a zero dimensional object cannot carry any angular momentum. More complicated singularities exist when you consider 5 dimensional general relativity and even more complicated ones when you work with string theory. For example, in models trying to construct a gravity/gauge dual to QCD it is necessary to consider a 7 dimensional object stretched through a space-time whose geometry is defined by a stack of 3 dimensional 'black branes', ie singularities but they have 3 spatial dimensions, not the zero of the Schwarzchild black hole. 'Black branes' are of considerable interest to theoretical physics. You said it had zero time duration, which is false. Something which has zero time duration is referred to in the literature as an 'instanton', ie it exists only for an instant.

That doesn't make any sense within a unified space-time structure. If an object were able to reach an event horizon then length contraction and time dilation would be infinite, making the black hole occupy a single point in space and in time. If singularities are a singular point in space-time (and there's absolutely no reason why they wouldn't be) then black holes are four dimensional hyperspheres. Do you have any experimental data at all to back up your assertion that singularities are single points in space but not in time?

6. That isn't even a question. Now we're into the realms of you just giving us your extremely dubious opinion about a realm of physics you have no experience with and which is often extremely counter intuitive. Likewise with 7,8,9 so I'll just skip them.

Don't to that. It makes it look suspiciously like you can't answer them.

Yes, we get it, you've just read some pop science book about black holes and now you want to tell everyone all the amazing knowledge you have. It's good you want to learn about these things, when I was 16-18 I too read all the pop science books in my local book store, but speaking as someone who has been on both sides of the fence (read lots of pop science but no knowledge of the actual models vs having knowledge of the actual models) I can tell you that pop science overviews do not bestow on you sufficient knowledge of the details to be able to start making assertions of the kind you are. As I've just explained, you've been wrong numerous times.

Oh behave. You've done no such thing you big fibber. All you've done is show that you're either unwilling or unable to engage in a meaningful debate so you parrot back some dodgy nonsensical physics without justifying it, ignore the points that you're unable to refute, and then attack me personally to try to discredit what I'm saying. What you're doing is very transparent.

They already are. That's what the principle of general covariance is all about. In the context of general relativity, when you 'feel' a local gravitational field, such as the gravitational field you feel standing on Earth, you are accelerating (in the sense that your proper acceleration, which is a relativistic invariant, is nonzero).

They're not anywhere near on an equal footing. Special relativity is only treated as a special case within the generalised structure of curved space-time. Gravity can supposedly accelerate objects to a relative velocity of above the speed of light, energy can't. In reality curved space-time can just as easily be viewed as flat space-time. There's absolutely no difference at all, it depends only on how you want to look at it.

(Incidentally, you don't accelerate due to "energy". That sounds like a misconception of highschool level physics. You accelerate due to the presence of a net force acting on you.)

What? That's like saying that objects don't fall, they gravitate towards mass. That's falling! You accelerate in the presence of energy. You also accelerate in the presence of mass. Energy accelerates you more, because E=mc^2, so K(ig) c^2 = K(og) where K is a subscript of curvature.You lot thought that I didn't know the maths didn't you? Well, you were right, a mathematician did that for me, although I actually could have done that myself looking at it. Even I can follow that one.

AlphaNumeric already answered this. I'll just point out that I happen to have given an answer to a similar question [POST=2629283]here[/POST] based on the Kruskal coordinate chart (which makes things particularly easy to visualise in this case). Short answer: objects can reach the event horizon in finite proper time (i.e. from the perspective of the object itself) and objects become irretrievable in finite time from the perspective of an external observer (in the sense that the point where the object crosses the event horizon drops eventually drops out of an external observer's future light cone).

Really? I've never heard that objects become irretrievable in a finite amount of proper time from the perspective of a more distant observer before. I thought that for it to become irretrievable, it would have to reach the event horizon? If that's true it would answer the rope paradox, if. Okay, so the question now becomes how can the point in space-time where the object reaches the event horizon drop out of the more distant objects light cone before the object reaches the event horizon from the more distant objects perspective?

A short answer is that the entire black hole solution, including the surrounding gravitational field, is a solution to the Einstein field equation (which basically defines GR). So a cheap answer is that this is allowed because general relativity predicts it, and the EFE "explains" how it is possible.

That said, there's a more intuitive answer. Basically, as has been mentioned elsewhere, an outside observer never sees matter cross the event horizon of a black hole (i.e. the point where the matter crosses the event horizon never drops out of an outside observer's past light cone) and that is also true of the matter that originally collapsed to form the black hole in the first place. So one way to think about it is that the gravitational field you're feeling isn't "created" by the black hole itself but rather all the matter that ever fell into it, about which information can still be reaching you indefinitely (because you never see matter actually cross the event horizon).

Nice answer. The matter close to the event horizon can't account for all the mass that's felt. The vast majority of it must be coming from the singularity.

General relativity also allows such a thing as an "eternal" black hole that isn't formed by matter collapse. In that case there's a different answer: it turns out that the Schwarzschild eternal black hole solution also requires the presence of a white hole in the causal past, which is sort of the opposite of a black hole (e.g. matter and light can't enter it and can only escape from it). So you can think of the gravitational field you feel around an eternal Schwarzschild black hole as being created by the corresponding white hole.

How does that one form then?

This is completely wrong. Actually it's probably better to think of the singularity as a 'surface' at a specific time but extended in space, which is how it appears in Kruskal-like charts. The idea of the event horizon as a point in space comes from the original description of the black hole solution in Schwarzschild coordinates. The problem is that Schwarzschild coordinates are a bit pathologically defined. Specifically, the Schwarzshild time and radial coordinates blow up on the event horizon and actually reverse roles inside the black hole. Within the event horizon, r is actually a timelike coordinate and t is actually a spacelike coordinate.

Yes I know. It's because time is at a right angle to the other dimensions, all four are at right angles to each other from the perspective of an inertial object. From the perspective of an accelerating object the angle is less. The angle shortens at a progressively slower rate if an object increases it acceleration at a constant rate in exactly the same way that an objects relative velocity increases if it's acceleration remains constant and the at the same rate that the four horizons approach at a progressively slower rate if an object increases it acceleration at a constant rate as I described before.

How is it completely wrong? Black holes are cone shaped in four dimensions according to the standard description. Trust me I'm very good at visualising four dimensions. That's how I was able to figure all this stuff amount for myself. They're not cone shaped though, they're spherical. Space and time are equivalent. It makes no sense for them to be longer in one dimension than they are in the others because black holes aren't like other objects that are made from atoms. They're much simpler.

The laws of physics aren't "supposed" to be anything except what they are, and a theory that "breaks" an external principle is not an internal inconsistency. As it happens, all the laws of physics that we know about, including general relativity, are time-reversible at the fundamental level, but we don't observe physics to be time-reversible at the macroscopic level. In many common, everyday scenarios, the time-reversed version of a macroscopic process is obviously thermodynamically impossible, which means that it is technically theoretically possible but extremely unlikely.

But gravity is still an attractive force when the arrow of time is reversed, so what gives?

I don't think you're thinking this through very carefully. White holes don't necessarily need to start. In classical physics, matter can't escape a black hole so a black hole that has formed simply continues to exist forever. The time-reversed version of that is a white hole that has simply always existed in the past, until all the matter constituting its mass escapes it.

Black holes do not exist forever! They're collapsing at the speed of light locally. The event horizon contracts at c, but slower as an inverse square of the distance as length contraction and time dilation increase from the perspectives of more distant observers.

Quantum field theory implies that black holes should eventually evaporate via Hawking radiation. The final stages of that evaporation aren't well understood with current physics (because we're getting into regimes where we need a theory of quantum gravity, which we don't have), but if you go with that and assuming the process is time-reversible, then you can imagine you could have white holes forming via some (probably extremely unlikely, but theoretically possible) process of "reverse Hawking radiation".

I've never understood Hawking radiation. A virtual anti-particle is created inside the event horizon, reducing the mass of the black hole? Since when to anti-particles have a negative mass? That's the theoretical and non-existent exotic particles, not anti-particles.

Who told you that? White holes don't actually repulse objects. It's just that their causal structure only allows one way travel out of the event horizon, just like the causal structure of a black hole only allows one way travel in. If you think of a black hole event horizon as expanding outward at the speed of light, then a white hole is the opposite of that. Just like with black holes, no actual "force" is involved.

Of course gravity is a force. Viewing as curved space-time doesn't change anything because it's exactly equivalent to flat space-time. If no object is allowed to reach an event horizon then there has to be an infinite repulsive force. Btw, all black hole that we 'see' are technically white holes. When a singularity forms the event horizon moves outwards at the speed of light locally but information propagates at the speed of light, so when an observer first becomes aware of the singularity the event horizon has already reached it's maximum size and is contracting at the speed of light locally, making the singularity appear larger from a distance and the difference in size becomes less pronounced over the same distance the further away the observer because it's an inverse square and making the singularity perfectly spherical in all four dimensions at any distance.

Hi, A-Wal. More info if you need it.

Thankyou.

Within the ergosphere space-time is dragged around faster than light - general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

No chance in hell! That's pseudo science bullcrap! Regions of space-time can move faster than light relative to other regions of space-time? Do you have any idea how ridiculous that sounds? You can't break the rules by viewing it as space-time moving instead of of objects moving through because it's the same bloody thing! They're equivalent. Grr.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary as seen by an external observer) because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

How the hell does that work? They hover, but not from the perspective of an external observer?

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way the black hole will spin more slowly and may even stop spinning eventually.

You mean slingshot?

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness - but remember that quantum mechanics does not allow objects to have zero size in any dimension (their wavefunction must spread), so general relativity's prediction is only the best idea we have until someone devises a theory which combines general relativity and quantum mechanics.

That's easy. All the physical processes of curved space-time can be expressed using flat space-time, thereby making gravity compatible with QM.

Possibility of escaping from a rotating black hole

Kerr's solution for the equations of general relativity predicts that:

The properties of space-time between the two event horizons allow objects to move only towards the singularity.
But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.
Passing through the ring shaped singularity may allow entry to a negative gravity universe.

:bugeye:

Tracy Hall
Posted: Nov 20 2006, 11:43 PM

Incidentally, McClintock is quoted as saying that a black hole is completely described by the two numbers (actually, a scalar and a vector) describing mass and spin, but it is my understanding that a black hole can also have a non-zero electrostatic charge, and thus it requires three quantities to completely describe it. Mass and spin all there are for practical purposes, though--I wouldn't expect a physically existing black hole to carry any measurable charge.

Yes, they're extremely simple objects. Much simpler than you lot are trying to make them.

AlphaNumeric
Posted: Nov 21 2006, 12:24 AM

Yep, by the 'No Hair Theorem' black holes are fantastically bland when it comes to their describing variables, just M (mass), J (=aM, a angular velocity) and Q (charge). The dynamics of the space-time in and around them though is very complex for depending on so few considerations!

No it isn't. It's very simple.

A little too simple for my taste, I don't see how the tick of a clock and time itself can be independent from each other.

Exactly!

 

[Captain Kremmen]

@A-Wal
Do you have the mathematics to back up your theories?
I mean that impressive squiggly stuff that professors write on blackboards.

 

[A-wal]

@A-Wal
Do you have the mathematics to back up your theories?
I mean that impressive squiggly stuff that professors write on blackboards.

Not yet. Oh, yes I do it's called special relativity. Gravity is the same but in reverse so the equations just need to be, er, turned round.