Gravity: The why and the how:

[The God]

In the first few lines of the paper linked above, the authors display the "river" metric (which, as they note, has a long history). That metric is a valid metric describing the Schwarzschild geometry, if I understand it correctly.

So, I'm still not seeing what your complaint is.

He has just started with the simplest of all the Schwarzchild Metric, that probably confused you to call it a river metric...


.............In the river model, space itself flows like a river through a flat background.....

This is what he says, now please tell me which 'metric' would have a flat background ? And what is that flat background ?

Why are you arguing ? Its a model for lay people to get some ideas about BH. Please don't call it a metric, which is a precise representation of 4-D spacetime geometry...

 

[Farsight]

No valid solution of Einstein's gravitational equations is popscience tosh. The "river" metric is a valid solution. Ergo, not popscience tosh.

It's absolute garbage. Einstein described a gravitational field as space that was "neither homogeneous nor isotropic", and modelled it as curved spacetime. He didn't say it was a place where "space itself flows like a river". That's ridiculous. It's a total travesty of GR. That metric is not a valid metric describing the Schwarzschild geometry. Note this on the Wikipedia article:

"Painlevé wrote to Einstein to introduce his solution and invited Einstein to Paris for a debate. In Einstein's reply letter (December 7),[6] he apologized for not being in a position to come soon and explained why he was not pleased with Painlevé's arguments, criticisms and solutions emphasising that the coordinates themselves have no meaning. Finally, Einstein came to Paris in early April. On the 5th of April 1922, in a debate at the "Collège de France" [7][8] with Painlevé, Becquerel, Brillouin, Cartan, De Donder, Hadamard, Langevin and Nordmann on "the infinite potentials", Einstein, baffled by the non quadratic cross term in the line element, rejected the Painlevé solution."

Einstein rejected them for good reason, and so do I. Because like Einstein said, a gravitational field is a place where the (coordinate) speed of light varies, at the event horizon it's zero, and it can't go lower than that.

 

[paddoboy]

He has just started with the simplest of all the Schwarzchild Metric, that probably confused you to call it a river metric...
.............In the river model, space itself flows like a river through a flat background.....This is what he says, now please tell me which 'metric' would have a flat background ? And what is that flat background ?
Why are you arguing ? Its a model for lay people to get some ideas about BH. Please don't call it a metric, which is a precise representation of 4-D spacetime geometry...

Oh Brother!!!

http://arxiv.org/pdf/gr-qc/0411060.pdf
Abstract:
This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

In summing, Professor Hamilton and his colleagues on his wb site also confirms that due to the more complicated nature of Reisnner-Nordstrom solution metric, he is working at this time is applying it to all BH's generally.
True as we all know since the simple Schwarzchild metric was formulated during the WW1, while Roy Kerr did not have a solution to the type that bears his name until 1963.
Yet this model is also applicable to Kerr type.

Perhaps you my friend [you meaning the god] would like to submit another paper correcting Professor Hamilton's paper.
I won't hold my breath though.

 

[paddoboy]

It's absolute garbage. Einstein described a gravitational field as space that was "neither homogeneous nor isotropic", and modelled it as curved spacetime. He didn't say it was a place where "space itself flows like a river". That's ridiculous.

Please Farsight! Stop embarrassing the great man. Sheesh!

 

[paddoboy]

The thing that our two friends need to realise is that the river/waterfall model is mathematically sound. And both our friends have shown continually a scrappy mistake ridden application of maths.

 

[The God]

.............In the river model, space itself flows like a river through a flat background.....

Those who think that it is a 'metric' then they can answer

Which metric would have a flat background ?
And what is that flat background ?
At 1.5 * EH the river flow speed would be 0.866c, the space is falling at this speed in so called river metric, how would you hold it ?


[In the paper Prof Hamilton has used the word 'metric' 16 times, not even once he called it a 'river metric'.]. It is a model and Prof himself warns that it is for those guys who lack in maths.

 

[James R]

He has just started with the simplest of all the Schwarzchild Metric...

and so... what?

............In the river model, space itself flows like a river through a flat background.....

This is what he says, now please tell me which 'metric' would have a flat background ?

Pretty much any metric you care to name. At large distances from a mass, spacetime is always approximately flat.

And what is that flat background ?

I like to call it the universe.

Why are you arguing ? Its a model for lay people to get some ideas about BH. Please don't call it a metric, which is a precise representation of 4-D spacetime geometry...

The maths is right there at the start of the paper. And it is a metric, whether you say it is or not. Do I need to cut and paste the maths for you?

 

[James R]

Farsight,

It's absolute garbage. Einstein ...

Einstein isn't the be-all and end-all of relativity. There's been almost 100 years of work on general relativity since Einstein. Why are you still stuck in 1916?

That metric is not a valid metric describing the Schwarzschild geometry.

What utter rot.

"Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole."
Link: https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates

Note this on the Wikipedia article...

You skipped over the maths of the article and just read the last paragraph, obviously.

Just because Einstein was baffled back in 1922 doesn't mean the solution isn't a perfectly valid description of the Schwrarzschild geometry.

Einstein rejected them for good reason, and so do I. Because like Einstein said, a gravitational field is a place where the (coordinate) speed of light varies, at the event horizon it's zero, and it can't go lower than that.

Nonsense.

 

[Farsight]

James R: I'm not "still stuck in 1916". I'm telling you straight: in a gravitational field space is not falling down. This notion that space itself flows like a river isn't 100 years of work on general relativity, it's cargo-cult woo. It's Chicken-Little woo. A gravitational field alters the motion of light and matter through space over time. It doesn't suck space in.

The Gullstrand-Painleve metric isn't valid because at the event horizon the coordinate speed of light is zero. You can't ignore this to define a coordinate system in a place where light doesn't move. This is why Einstein said the coordinates themselves have no meaning.

 

[origin]

A gravitational field alters the motion of light and matter through space over time

That is an alternate theory of yours. Mainstream physics (which by definition is not woo) says that space is warped by gravity and light bends because it follows the curvature of space.

 

[James R]

I'm telling you straight: in a gravitational field space is not falling down.

It doesn't matter what your opinion is. The "river" metric presented contains a valid set of coordinates that describe the Schwarzschild metric. Those describe space falling down. They are as valid as the Schwarzschild coordinates. Recall that general relativity is a coordinate-independent theory.

This notion that space itself flows like a river isn't 100 years of work on general relativity, it's cargo-cult woo.

Until you can find a flaw in the paper that was posted, you have no right to make that claim.

But you can't follow the mathematics, can you? You have no idea what a metric is, or how GR works mathematically. All you have is pretty pictures, an active imagination and a pop-science level of knowledge about GR that fails you as soon as you try to do anything meaningful with it.

The Gullstrand-Painleve metric isn't valid because at the event horizon the coordinate speed of light is zero.

No it's not. It's $$c$$ in that metric.

You can't ignore this to define a coordinate system in a place where light doesn't move.

Light happily crosses the event horizon of a black hole. The usual Schwarzschild geometry has a removable coordinate singularity at the event horizon. That word "removable" tells us that there's no physical problem at the horizon - just a problem with those particular coordinates. The "river" metric avoids the problem there quite nicely. So do the Kruskal-Sekeres coordinates, and various other choices of coordinates.

This is why Einstein said the coordinates themselves have no meaning.

Indeed.

If only you understood what Einstein really meant by that.

 

[Schmelzer]

The thing that our two friends need to realise is that the river/waterfall model is mathematically sound.

There is something to object to the model.

A river is something with a conservation law. There is a flow, defined by a vector field, and there is also a conservation law of what flows. In the river model proposed there is no analogon of such a conservation law. Thus, to name this model a "river model" is misleading, suggests an association (a conserved flow) which is not realized.

Then, the suggested picture is far away from being a general one, it works only for very special solutions.

 

[Farsight]

That is an alternate theory of yours. Mainstream physics (which by definition is not woo) says that space is warped by gravity and light bends because it follows the curvature of space.

That isn't mainstream, because it isn't true. Mainstream physics says gravity results in curved spacetime, as per this depiction of Riemann curvature:

CCASA image by Johnstone, see Wikipedia

Light curves because of the "spacetime tilt". See the tilted light cones in this Stanford article. If your spacetime is flat horizontal board, light goes straight. If you tilt the board, it doesn't. It curves like a marble would curve if you rolled it across the board. The steeper the slope, the more light curves. Look again at the picture above, and imagine it's the board. The curvature you can see is curved spacetime. If this isn't there, the whole board is flat and horizontal. So spacetime curvature is the "defining feature" of a gravitational field. Hence in this Baez article you can read this: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial". Note that light doesn't curve because space is curved. It curves because spacetime is tilted. And the physical reality that underlies this is inhomogeneous space. Not curved space, inhomogeneous space:

 

[Farsight]

It doesn't matter what your opinion is. The "river" metric presented contains a valid set of coordinates that describe the Schwarzschild metric. Those describe space falling down. They are as valid as the Schwarzschild coordinates.

You can use any coordinates you choose, but don't kid yourself that they describe reality, because space isn't falling down.

Recall that general relativity is a coordinate-independent theory.

Yes, but when you adopt a new coordinate system, it doesn't change reality. The inhomogeneous space that comprises a gravitational field is not magically converted into falling-down space.

Until you can find a flaw in the paper that was posted, you have no right to make that claim.

I told you the flaw. When light doesn't move you have no coordinates. It's a mathematical fiction to pretend that you have.

But you can't follow the mathematics, can you? You have no idea what a metric is, or how GR works mathematically. All you have is pretty pictures, an active imagination and a pop-science level of knowledge about GR that fails you as soon as you try to do anything meaningful with it.

I can follow the mathematics, I'm the one who actually understands it. I do know what a metric is. I'm not the one with the pop-science understanding.

No it's not. It's c in that metric.

So we'll all sit here watching you measuring the speed of light at that location. Let's wait a year. Have you measured it to be c yet? No, not yet, because of the infinite gravitatioanl time dilation. Let's wait a million years. Have you measured it to be c yet? No, not yet, because of the infinite gravitatioanl time dilation. Let's wait a billion years. Have you measured it to be c yet? No, not yet, because of the infinite gravitatioal time dilation. You never ever measure it. The idea that you do is a mathematical fantasy. It's a fairy tale.n

Light happily crosses the event horizon of a black hole. The usual Schwarzschild geometry has a removable coordinate singularity at the event horizon. That word "removable" tells us that there's no physical problem at the horizon - just a problem with those particular coordinates. The "river" metric avoids the problem there quite nicely. So do the Kruskal-Sekeres coordinates, and various other choices of coordinates.

And they all suffer from the same problem. Perhaps we need to discuss why the light doesn't get out again:

You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic gedanken wand and make the planet denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive, and take it to the limit such that it's a black hole. At no point did the light ever curve round, or slow down as it ascends, or fall down. So why doesn't the light get out?

 

[Schmelzer]

You can use any coordinates you choose, but don't kid yourself that they describe reality, because space isn't falling down.

This is, indeed, a point. The coordinates are fine, the metaphysical description in terms of a space flowing like a river is invalid.

So we'll all sit here watching you measuring the speed of light at that location. Let's wait a year. Have you measured it to be c yet? No, not yet, because of the infinite gravitatioanl time dilation. Let's wait a million years. Have you measured it to be c yet? No, not yet, because of the infinite gravitatioanl time dilation.

What would really happen, in the spacetime interpretation of GR, would be different. Say, A is on the horizon. Not for long, because he consists of usual matter. Thus, he would be infalling. Following the equivalence principle, he would not even know about this (except if the tidal forces would be too strong). Then, if he wants to measure some speed, he would try to create a local system of coordinates, stupidly with assuming himself being at rest. This would be a system of coordinates quite different from that with the light ray being at rest. In this strange, infalling system of coordinates the light would have, by construction, the speed c.

The GR spacetime interpretation may be rejected as stupid or unreasonable, if one likes, but not as inconsistent. It is quite consistent.

 

[OnlyMe]

No valid solution of Einstein's gravitational equations is popscience tosh. The "river" metric is a valid solution. Ergo, not popscience tosh.

James.., if general relativity is a description of a real gravitational field, which is where it, general relativity, began.., would that not mean that while we can learn from mathematically valid hypotheticals, that are not observed to represent any real gravitational field.., only solutions that do represent real gravitational fields are valid solutions?

And yes your statement above is technically accurate because even solutions that do not describe anything expected to be real, can be mathematically valid.

The link to, http://jila.colorado.edu/~ajsh/insidebh/rn.html, has been used to validate the idea of a charged black hole and how it interacts with our reality. The problem is in the third paragraph into the link,

The big difference between a charged (Reissner-Nordström) and an uncharged (Schwarzschild) black hole is that the mathematical solution to the charged black hole has, inside its horizon, a one-way wormhole that connects to a white hole that propels you to another space and time. Sadly, the wormhole is violently unstable, and would not occur in reality. Click on Waterfall to learn more about why the charged black hole has a wormhole. Click on Realistic to see what happens in reality,​

The above seems to clealy state that the charged black hole does not exist in reality. Not that they are rare, that they do not exist!

The question boils down to what the term valid applies to, reality or a mathematically valid solution. Many solutions may be mathematically valid and yet describe things that are known not to be real. Because these discussions include many different mathematically valid solutions, side by side (even intermingled), as descriptions of reality, there can be no expectation of ever reaching any consensus, in the argument... And I intentionally use the word argument, because much of the argument is directed at the posters rather than any specific discussion of a solution to EFE.

 

[paddoboy]

James R: I'm not "still stuck in 1916". I'm telling you straight: in a gravitational field space is not falling down. This notion that space itself flows like a river isn't 100 years of work on general relativity, it's cargo-cult woo. It's Chicken-Little woo.

And yet it is you, not me, or not James that has been banned constantly from many forums for preaching woo.
Let me again tell you [and other alternative nuts] that if any of you had anything of substance, you would not be here. You would be making preparations for next years Nobel.
It's only forums such as this where your woo is even considered.
On that score, you are a fraud Farsight.

 

[paddoboy]

Why are you arguing ? Its a model for lay people to get some ideas about BH. Please don't call it a metric, which is a precise representation of 4-D spacetime geometry...

And as such you need to pay more attention to it as a lay person, and considering you fail to recognise that total compulsory collapse happens after Schwarzchild radius is breached, and that tidal gravity effects will logically overcome all other forces as it moves to infinity, and that cosmologists are able, and do assign reasonable properties to within a BH, and that charge and spin are negated over time, I suggest far more than most other lay people that are able to understand and accept these concepts.

 

[paddoboy]

If only you understood what Einstein really meant by that.

One can live in hope! [fingers crossed, toes crossed ]

 

[paddoboy]

This is, indeed, a point. The coordinates are fine, the metaphysical description in terms of a space flowing like a river is invalid.

The river/waterfall model is mathematically validated and has been accepted by arxiv
Actually interesting that you decide to hop onto the crank bandwagon, considering that you claim your own "ether"paper by the same publisher predicts more than mainstream interpretation of GR.
I smell some hypocrisy.