Black hole matter accumulation

[zonde]

And as for my statement that the Schwarzschild Metric is not correct - I can think of two people who agree with me: Einstein and Schwarzschild.

It seems you have misunderstood something about applicability of Schwarzschild Metric. It does not describe (only) black holes. It describes gravitation around non-rotating spherically symmetric object. Only when we assume that radius of gravitating object is smaller than Schwarzschild radius we get black hole (and can speak about possible breakdown of model).
But otherwise it is tested and it works.

 

[PeterDonis]

Good coordinate chart does not contain empirically meaningless regions of spacetime i.e. it does not make untestable pseidoscientific implications.

"Behind an event horizon" does not automatically equal "empirically meaningless". In this particular case, unless you add the additional claim that worldlines can just "end" at the horizon (see below for more on that), then there has to be *something* behind the horizon--some additional region of spacetime there, even if no causal influence can propagate from that region to the exterior.

If coordinate chart breaks down at some point we simply say that it's domain of applicability ends there. Beyond that point live dragons.

But there are plenty of coordinate charts that do *not* break down at the horizon. The fact that one does (the Schwarzschild chart) does not imply that spacetime itself breaks down. Physical invariants at the horizon are perfectly finite and well-behaved. See my previous post in answer to ?.

So let's assume that I take Schwarzschild coordinate chart and use the same mathematical manipulations that are used in construction of Gullstrand–Painleve coordinates. But instead of coming up with coordinates that describe interior of black hole I get coordinates that correspond to white hole interior

You don't have to assume this; it's been done. There are two Painleve charts, an "ingoing" and an "outgoing" one; the same is true of the Eddington-Finkelstein chart. However, the two charts are not contradictory because the "interior" portions of the ingoing and outgoing charts describe different regions of spacetime. The white hole interior region is a *different* interior region than the black hole interior region. The maximally extended Kruskal chart makes all this clear and easy to visualize.

Btw, I should note that for a black hole that forms from a collapsing star, the spacetime does not contain a white hole interior region. So even though the outgoing Painleve and Eddington-Finkelstein charts can be constructed mathematically, they would not be very useful for describing such a spacetime, because they would not describe the black hole interior, and they would be "cut off" by the non-vacuum portion of the spacetime (the collapsing star) well before the point where the white hole horizon would exist.

The Penrose diagrams at the following URL on Wikipedia give a good visual of what I've said:

http://en.wikipedia.org/wiki/File:PENROSE2.PNG

Compare the "static grey wormhole" diagram with the "actual black hole from collapsing star" diagram.

Could I argue in this case that region inside the horizon does not exist?

No, for the reason I just gave above.

Outgoing null worldlines can stay there without moving anywhere. And they don't cease to exist because of that.

Yes, but there are plenty of other null worldlines at any given event, including events on the horizon, besides the outgoing ones. You'll note that I specified *ingoing* null worldlines in my post.

In case of massive object you have it's proper time. You are assuming that proper time should extend to infinity. If proper time does not extend further beyond certain value it means that object ceased to exist.
Well you can't apply the same reasoning to light. Light does not have proper time.

No, but you can still construct an affine parameter along a null worldline that does not have the same value everywhere. It just won't have a physical interpretation as proper time. But the same reasoning about proper time extending to infinity as long as the curvature and other physical quantities are finite and well-behaved, also applies to the affine parameter of a null worldline: it should extend to infinity as long as the curvature and other physical quantities are finite and well-behaved.

If you really want to claim that spacetime ends at the horizon, you need to show either that (a) some physical quantity at the horizon is *not* finite and well-behaved, or (b) worldlines (either timelike or null) can "end" at a finite value of their affine parameter (proper time is an affine parameter for timelike worldlines) even though all physical quantities are finite and well-behaved there. So far you haven't advanced an argument for either of those propositions. Do you have one?

Besides we can say that at EH massive particles become photon like and that's the reason why they proper time does not increase.

No, we can't say that because it isn't true. Massive particles continue to travel on timelike worldlines at and inside the horizon.

Can't say that I am really interested in that but if I can't check it I am not buying it.
Maybe we can try to leave out this point from our discussion for now? I will try to look for some online resources.

Or check out any good relativity textbook. When I have a chance to haul out my copy of MTW I can give you a page reference.

I don't mind leaving this point out of the discussion, as long as you're not disputing the fact that physical covariant and invariant quantities, like the curvature tensor, are finite and well-behaved at the horizon. If you're going to dispute that then we need to resolve it because otherwise we'll be talking past each other. The fact that physical covariant and invariant quantities are finite and well-behaved at the horizon is a key point in the arguments I've been making, as you can see from earlier in this post.

 

[PeterDonis]

Lengthy discussions around Schwarzschild Metric might indicate that there is no consensus yet about it's domain of applicability.

You may be misunderstanding some of the discussion, or I may be misunderstanding how you are using the term "Schwarzschild Metric". Nobody is disputing the domain of applicability of the Schwarzschild "metric", if by that you mean the exterior Schwarzschild coordinate chart and the expression of the metric in that chart. I believe we are all in agreement that that coordinate chart and its expression of the metric are only applicable outside the horizon.

The dispute, in so far as there is one, appears to me to be about whether the *spacetime geometry* around a black hole "ends" at the horizon, or whether there is a region of that spacetime inside the horizon. If that's a question about domain of applicability, it's about the domain of applicability of the geometry, as a mathematical object, to a physical spacetime; mathematically there is no question that there exists a spacetime geometry that includes both the exterior and black hole interior regions. The question is whether the black hole region of the mathematical object corresponds to an actual physical region of the spacetime around a black hole.

 

[PeterDonis]

Someone felt it was necessary to formulate this link and pay for its continued presence on the web. That means that others have asked the same question about gravity escaping from black holes that I posed. Not only that, but these must have been credible persons and this questioning must have come up repeatedly over the years. If my question was not a legitimate issue, then no link would be necessary.

If by "legitimate issue" you just mean "a legitimate question to ask, with a legitimate, generally accepted answer that is consistent with GR", then that's fine. If by "legitimate issue" you mean "there is an answer given on this web page, but it's not a generally accepted answer in relativity physics so it's OK to dispute it without having *really* good backup", then I don't think that's an accurate characterization of the state of this area of physics. See below.

As far as why this FAQ entry is on the web, remember that the Usenet Physics FAQ is not for professional physicists; it's for ordinary lay people, to give short summaries of what is generally accepted among physicists in terms that lay people can understand. It's particularly intended to provide short summaries of the generally accepted answers to questions that lay people often ask because they have not yet fully grokked the conceptual shifts you have to make to understand modern physics. You might want to read the index page of the FAQ to get an idea of why it's there and where the writers are coming from:

http://www.desy.de/user/projects/Physics/index.html

And as for my statement that the Schwarzschild Metric is not correct - I can think of two people who agree with me: Einstein and Schwarzschild. Unfortunately, this disagreement has been going on for ninety years and shows no signs of being resolved any time soon. I think that it is appropriate to mention, at least in passing, that theories that are often thought of as confirmed science are not so universally agreed upon.

Einstein and Schwarzschild worked years and years ago; a *lot* of knowledge has been gained since they made their objections, and the reasons why their objections are no longer considered valid are well understood. Can you give any recent credible references for physicists who doubt that there is an interior region in the actual, physical spacetime surrounding a black hole? My understanding is that the web page I linked to is a good short summary of what is generally accepted among relativity physicists, and that the issue we are debating in this thread is *not* seriously debated in the physics community. Which is *not* to say that we have any actual experimental evidence from events that happened inside a black hole horizon; that would be impossible, and the theory explains why. But there is plenty of indirect evidence that the spacetime around a black hole does not just "end" at the horizon.

 

[Passionflower]

Which is *not* to say that we have any actual experimental evidence from events that happened inside a black hole horizon; that would be impossible, and the theory explains why. But there is plenty of indirect evidence that the spacetime around a black hole does not just "end" at the horizon.

If we want to stay "mathematical" and talk about the Schwarzschild solution the interior solution is almost never discarded as unphysical, however most scientist seem to have no qualms about cutting the "obviously unphysical" parts of the KS coordinate chart. Is that consistent in your opinion?

At any rate the Schwarzschild solution is a mathematical model of a theory. If we cannot possibly get any information about the interior region we cannot apply the scientific method and the whole argument is academic.

 

[PeterDonis]

If we want to stay "mathematical" and talk about the Schwarzschild solution the interior solution is almost never discarded as unphysical, however most scientist seem to have no qualms about cutting the "obviously unphysical" parts of the KS coordinate chart. Is that consistent in your opinion?

As I understand it, the cutting of "obviously unphysical" parts of the KS chart occurs because those portions are "overwritten" by the non-vacuum region of spacetime occupied by the collapsing object that forms the black hole. The black hole interior region is only "partly overwritten" by the collapsing object, so there is still a black hole interior in the actual, physical spacetime. The Penrose diagram I linked to earlier hopefully makes my hand-waving expressions just now easier to visualize.

At any rate the Schwarzschild solution is a mathematical model of a theory. If we cannot possibly get any information about the interior region we cannot apply the scientific method and the whole argument is academic.

Saying that events in the interior cannot causally influence events in the exterior is not the same as saying we can get no information about the interior. There may be indirect ways of doing so. One could also argue, though, that, since the interior can't causally influence the exterior, it doesn't *matter* what goes on in the interior, which would do equally well at making the argument academic. So I think I agree with you that it's academic.

 

[Dale]

Seems interesting. What coordinate chart would you prefer for discussion purposes as an alternative to Schwarzschild coordinates?
I have looked at Gullstrand–Painleve coordinates and I suppose that I understood more or less what they are doing but I don't know how popular they are.

Sorry I have been away from this thread for a bit, but I would make the same suggestions that Peter did:
Gullstrand-Painleve
Eddington-Finkelstein
Kruskal-Szekeres

 

[PAllen]

I will open a new set of arguments on this topic. Somehow, I had forgotten developments I was following a number of years ago that have direct bearing on this debate. To wit, these issues may be quite testable and not academic.

As a preliminary observation, in a perfectly symmetric gravitational collapse (which implies, as has been noted, no white hole region), the actual predictions of GR (by definition coordinate independent) describe the horizon as purely optical phenomenon, not unlike gravitational lensing. We don't treat the lensed image as 'best description of reality'. Instead, understanding GR, we posit a more plausible reality behind the lensing. Similarly, GR taken literally asks us to understand the horizon as a frozen optical image, behind which perfectly normal physical processes occur (until the true singularity).

As a follow on to this, let us ask what would be seen if a globular cluster slowly coalesced to the point where it became a super massive black hole in a hypothetical dust free environment, with no stellar collisions occurring before horizon formation. My understanding of what we would see is a slowly compressing cluster brightening normally (same light, smaller area of image) until, at some point, motion slows down, emissions get redder and weaker (still looking like a cluster of stars), until, in finite time, the whole cluster has effectively vanished (all light so redshifted and emission rates so low, that no conceivable instrument can detect light from it anymore). Do we suppose that a globular cluster has vanished from the universe, or believe GR that perfectly ordinary physics is continuing that we just can't see? [and the only physics for what we can't see, consistent with GR, is further collapse].

Finally(!) my main point, alluded to in my intro, is that there is reasonable likelihood that the cosmic censorship hypothesis is simply false. In which case, the physics of what happens close to the true singularity may be accessible; at some point QG alternatives to the singularity may be testable. Then, one must ask, if there are cases we can see the physics of the final state of collapse, and others where an optical horizon prevents it, do we assume the latter represents fundamentally different physics, or do we believe GR that it is just an optical effect?

Here are some references on the doubtful nature of cosmic censorship, and the ideas of testing it:

http://prd.aps.org/abstract/PRD/v19/i8/p2239_1
http://arxiv.org/abs/gr-qc/9910108
http://arxiv.org/abs/0706.0132
http://arxiv.org/abs/gr-qc/0608136
http://arxiv.org/abs/gr-qc/0407109

 

[?????]

the issue we are debating in this thread is *not* seriously debated in the physics community. Which is *not* to say that we have any actual experimental evidence from events that happened inside a black hole horizon; that would be impossible, and the theory explains why.

Let me paraphrase what you said. Someone has a theory that XXX happens, and this theory states that it is impossible to prove (and, by implication, to disprove) the theory. Therefore the theory must be correct.

This is what results when you start with a mathematical model containing a singularity. That's what Einstein objected to 80 years ago and mathematical singularities haven't been given legitimacy since then.

The Schwarzschild Solution seeks to describe what happens to some tiny object as it falls from infinity to a single isolated planet within an empty universe. But as that object gets near the Schwarzschild Radius, no matter how tiny, it's mass blows up to astronomical values. The planet is no longer the only mass in the universe and the GR cannot solve the problem. Everything derived after that requires careful review, no matter how prestigious the current group of supporters are.

 

[Passionflower]

The Schwarzschild Solution seeks to describe what happens to some tiny object as it falls from infinity to a single isolated planet within an empty universe. But as that object gets near the Schwarzschild Radius, no matter how tiny, it's mass blows up to astronomical values.

Rest mass stays the same however I agree that a test mass can hardly be called a test mass when it reaches or even passes the EH.

The theory has all kinds of challenges, from Cauchy surfaces to incomplete geodesics to interactions at infinity to how to even begin to describe initial values. Even computer simulations run often into big problems.

I believe Einstein, if he were alive today, would be the first to admit that and I believe he would abhor opinions from people who claim GR has no issues whatsoever and is as solid as a rock, opinions I believe that are mostly promoted by what I think are "career educators".

 

[Dale]

Let me paraphrase what you said. Someone has a theory that XXX happens, and this theory states that it is impossible to prove (and, by implication, to disprove) the theory. Therefore the theory must be correct.

Don't be silly. GR is falsifiable. What we have is a theory that says U, V, W, X, Y, and Z happen, of those U, V, and W have been observed and reported, X and Y can be observed in principle but have not yet, and Z can in principle be observed but not reported.

This is not even remotely a case of an unfalsifiable theory.

 

[DrGreg]

I would like to suggest to all those who have difficulty in accepting the established description of what happens at or inside the event horizon of a black hole should spend some time investigating the Rindler horizon that occurs when an observer undergoes the "pseudogravity" of constant proper acceleration in flat spacetime (i.e. with no gravitation). I described this in post #75 of this thread. That particular post was aimed at A-wal so I deliberately avoid any maths. But the graph there is no sketch: it was plotted accurately by computer using the correct relativistic formulas for Rindler coordinates.

The event horizon of a black hole is both an "apparent horizon" and an "absolute horizon" in the jargon. A Rindler horizon is also an "apparent horizon" but not an "absolute horizon". I think all the properties of horizons that have been questioned in this thread are properties of apparent horizons rather than absolute horizons. The big advantage of a Rindler horizon is that if you get confused you can always examine it using Minkowski coordinates (I would hope anyone trying to learn GR would already have a reasonably good understanding of Minkowski coordinates in SR).

In particular it ought to be clear that:

• the inside of a Rindler horizon really does exist
• an inertial particle, initially a finite distance from the Rindler horizon, reaches it in finite proper time, passes through it without incident and continues beyond it, and measures the relative speed of the horizon to be c
• that same particle takes an infinite amount of Rindler-coordinate-time to reach the horizon
• the Rindler observer visually sees the particle slow down asymptotically to zero speed at the horizon, asymptotically red shifted to zero frequency and never seen to cross the horizon
• Rindler coordinates suffer a coordinate singularity at the horizon and do not reach it or persist beyond it
• at the Rindler horizon there is no singularity in Minkowski coordinates (which cover both sides of the horizon and the horizon itself)

Just to spell out the relationship clearly:

• Rindler coordinates for a Rindler horizon are the equivalent of Schwartzschild coordinates for a Schwartzschild horizon
• Minkowski coordinates for a Rindler horizon are the equivalent of Kruskal–Szekeres coordinates for a Schwartzschild horizon

 

[Dale]

At any rate the Schwarzschild solution is a mathematical model of a theory. If we cannot possibly get any information about the interior region we cannot apply the scientific method and the whole argument is academic.

In principle you can apply the scientific method to the interior of the horizon, you just cannot ever publish the results.

 

[PeterDonis]

Let me paraphrase what you said. Someone has a theory that XXX happens, and this theory states that it is impossible to prove (and, by implication, to disprove) the theory. Therefore the theory must be correct.

Your paraphrase is incorrect. What I said was: we have a theory that there is a region of spacetime behind the event horizon of a black hole. Since if the theory is correct, the region of spacetime behind the event horizon cannot have any causal influence on the region outside the horizon, it is impossible to prove the theory by receiving causal influences from the region behind the horizon. That's all I said. I did *not* say, or imply, that it is impossible to prove (or more precisely, to get experimental support for--scientific theories are never "proved") the theory by any means whatsoever.

I also did not say that it is impossible to disprove the theory. That would be easy: just run an experiment whose results show causal influences being received from an infalling object past the point where the theory says no causal influences can be received. If such an experiment is ever done, GR (or at least this solution of it) will have to be revised.

This is what results when you start with a mathematical model containing a singularity. That's what Einstein objected to 80 years ago and mathematical singularities haven't been given legitimacy since then.

First of all, on this particular issue, Einstein was wrong. Simple as that. He was Einstein, not infallible. Einstein did not know about the Painleve chart, or the Eddington-Finkelstein chart, or the Kruskal chart. He did not understand the full nature of the spacetime geometry of the Schwarzschild solution. Today we understand it a lot better, and can make arguments that would have convinced Einstein himself, if he were consistent with other things he had said--for example, he repeatedly said that particular coordinate charts don't matter, what matters are the covariant and invariant objects, like the curvature tensor. So if he were consistent, then pointing out to him that the curvature tensor is finite and non-singular at the horizon could have convinced him to re-evaluate his skepticism about gravitational collapse.

Einstein wasn't alone in not understanding the Schwarzschild geometry fully in the 1930's; nobody really did. Oppenheimer and Snyder didn't fully understand it either when they published their 1939 paper on gravitational collapse. They made a gut call that the collapse was genuine, even though they could see the mathematical singularity in one particular set of coordinates. Einstein made a gut call the other way. He called it wrong. It happens. (It happened to Einstein himself in at least one other case related to GR, his attempt to find a static solution for the universe as a whole. If he had followed his own equations to their logical conclusion, he could have predicted the expansion of the universe well before it was discovered. He didn't. He later called this "the greatest blunder of my life".)

Moreover, you are putting an awful lot of weight on "mathematical singularities" being somehow a sign of complete breakdown. They're not. There are plenty of ways to handle them, such as taking limits or switching coordinate charts, in order to calculate the actual physical covariant and invariant quantities and show that they are non-singular. Such things are perfectly legitimate mathematically and physically. There are singularities that aren't amenable to such treatment, such as the curvature singularity at r = 0 in Schwarzschild spacetime. But the coordinate singularity at r = 2M is not one of them.

The Schwarzschild Solution seeks to describe what happens to some tiny object as it falls from infinity to a single isolated planet within an empty universe. But as that object gets near the Schwarzschild Radius, no matter how tiny, it's mass blows up to astronomical values. The planet is no longer the only mass in the universe and the GR cannot solve the problem. Everything derived after that requires careful review, no matter how prestigious the current group of supporters are.

Where are you getting this from? How does the falling object's mass increase? If you're referring to "relativistic mass", that doesn't affect the gravitational field or the spacetime curvature; if the object was too small to make a difference to the curvature far away, it's still too small to make a difference when it reaches the horizon.

 

[Passionflower]

In principle you can apply the scientific method to the interior of the horizon, you just cannot ever publish the results.

Only if it exists, and since we cannot know by experiment it really exists we canot use the scientific method. It would be like claiming "heaven exists, all who go there will agree however they are not able to communicate their findings".

 

[PeterDonis]

Rest mass stays the same however I agree that a test mass can hardly be called a test mass when it reaches or even passes the EH.

Why not?

The theory has all kinds of challenges, from Cauchy surfaces to incomplete geodesics to interactions at infinity to how to even begin to describe initial values. Even computer simulations run often into big problems.

I believe Einstein, if he were alive today, would be the first to admit that and I believe he would abhor opinions from people who claim GR has no issues whatsoever and is as solid as a rock, opinions I believe that are mostly promoted by what I think are "career educators".

I am not claiming that GR has no issues whatsoever. I am claiming that the purported issues being brought up by other posters I've been responding to are not issues, they are just misunderstandings.

Also, even with all the problems you raise, as far as I know, whenever predictions have been extracted about gravitational collapse, with the idealizations of the Schwarzschild geometry removed (e.g., no exact spherical symmetry), the key feature of the event horizon and an interior region behind it are still there. I'm not aware of *any* solution, even an approximate computer-generated one, that shows spacetime just stopping at the horizon. Even theories where lots of ongoing work is being done on issues like the ones you raise can still yield robust predictions. I am claiming that GR's prediction of a black hole event horizon with an interior region behind it is such a robust prediction.

 

[Passionflower]

I also did not say that it is impossible to disprove the theory. That would be easy: just run an experiment whose results show causal influences being received from an infalling object past the point where the theory says no causal influences can be received. If such an experiment is ever done, GR (or at least this solution of it) will have to be revised.

If we use an object that is massive enough to make any potential impact on a BH then clearly we could not use the Schwazschild solution.

Frankly I do not understand this defensive approach. Einstein's general relativity is a masterpiece and clearly very useful but that does not mean that every single iota must be correct and that those who question parts which have never been empirically verified or perhaps can never be empirically verified are automatically idiots. When we take theories as dogmas then any potential for progress stops IMHO.

 

[Q-reeus]

If Schwarzschild metric correctly describes reality exterior to a static spherical gravitating body, it ought not lead to a rediculous paradox. So consider a thin spherical shell, outer radius r_b, inner radius r_a. Everyone agrees that interior to r_a there is everywhere an equipotential region and consequently the flat Minkowski metric applies. Which means isotropy of length scale; so in spherical coords; dr = r*sin(θ)*d∅ = r*dθ. Exterior to r_b however, Schwarzschild metric is supposed to apply, and an examination shows that, strangely some would say, in coordinate measure, while tangent length scale is completely impervious to gravity, radial measure (and equally, clock-rate) is contracted by the factor 1-r_s/r, with r_s the gravitational radius 2GM/(c²). The interesting part is attempting a physically sensible transition - a boundary match from exterior Schwarzschild to interior Minkowski metric. Clearly the tangent components of length scale will sail through from rb to ra unaltered, but this cannot be for the radial component - otherwise the interior could not be flat. Hence to satisfy interior Minkowski flatness, the radial length measure must 'magically' lose all its dependence on gravitational potential in just traversing the distance r_b-r_a, despite working hard to have built it up in coming all the way from infinity down to the radius r_b! This makes physical sense? Now given that clock-rate and radial length have exactly the same functional dependence on potential exterior to r_b, what are we supposed to assume will apply to clock-rate interior to r_a? Most everyone expects that clock-rate should be depressed by just the 1-r_s/r factor. After all, the notion that redshift (ie depressed clock-rate of emitter) could disappear as one lowered a light source through a small hole in the shell seems ludicrous. But then so does the notion that nature stands at the shell exterior like some cosmic traffic cop, waving clock-rate through unmolested just as for tangent length scale, but forcing radial measure to undergo an abrupt transition back to its 'infinity' zero-potential value.
Hello - is something wrong here!? Anyone spot an elephant in the room? Could the culprit here be the Schwarzschild metric, and that which it is derived from? Maybe I'm stupid or something and got all the above totally wrong, but looks to me only one metric can yield a physically sensible transition - an isometric one where all length scale and clock-rate components are equally affected by gravitational potential. Only one I'm aware that does that is Yilmaz gravity, but since it's so savagely bagged by GR supporters, I guess it just must be crackpot nonsense. Well something is. :zzz:

 

[PAllen]

If Schwarzschild metric correctly describes reality exterior to a static spherical gravitating body, it ought not lead to a rediculous paradox. So consider a thin spherical shell, outer radius r_b, inner radius r_a. Everyone agrees that interior to r_a there is everywhere an equipotential region and consequently the flat Minkowski metric applies. Which means isotropy of length scale; so in spherical coords; dr = r*sin(θ)*d∅ = r*dθ. Exterior to r_b however, Schwarzschild metric is supposed to apply, and an examination shows that, strangely some would say, in coordinate measure, while tangent length scale is completely impervious to gravity, radial measure (and equally, clock-rate) is contracted by the factor 1-r_s/r, with r_s the gravitational radius 2GM/(c²). The interesting part is attempting a physically sensible transition - a boundary match from exterior Schwarzschild to interior Minkowski metric. Clearly the tangent components of length scale will sail through from rb to ra unaltered, but this cannot be for the radial component - otherwise the interior could not be flat. Hence to satisfy interior Minkowski flatness, the radial length measure must 'magically' lose all its dependence on gravitational potential in just traversing the distance r_b-r_a, despite working hard to have built it up in coming all the way from infinity down to the radius r_b! This makes physical sense? Now given that clock-rate and radial length have exactly the same functional dependence on potential exterior to r_b, what are we supposed to assume will apply to clock-rate interior to r_a? Most everyone expects that clock-rate should be depressed by just the 1-r_s/r factor. After all, the notion that redshift (ie depressed clock-rate of emitter) could disappear as one lowered a light source through a small hole in the shell seems ludicrous. But then so does the notion that nature stands at the shell exterior like some cosmic traffic cop, waving clock-rate through unmolested just as for tangent length scale, but forcing radial measure to undergo an abrupt transition back to its 'infinity' zero-potential value.
Hello - is something wrong here!? Anyone spot an elephant in the room? Could the culprit here be the Schwarzschild metric, and that which it is derived from? Maybe I'm stupid or something and got all the above totally wrong, but looks to me only one metric can yield a physically sensible transition - an isometric one where all length scale and clock-rate components are equally affected by gravitational potential. Only one I'm aware that does that is Yilmaz gravity, but since it's so savagely bagged by GR supporters, I guess it just must be crackpot nonsense. Well something is. :zzz:

Please describe the above in reference to istotropic Schwarzschild coordinates. Coordinates have nothing to do with physical predictions. The isotropic Schwarzschild coordinates describe the same manifold, but are istotropic everywherea, at all times.

 

[Dale]

Only if it exists, and since we cannot know by experiment it really exists we canot use the scientific method.

You can use the scientific method and determine by experiment that it exists. There is nothing in principle that prevents such an experiment.

It would be like claiming "heaven exists, all who go there will agree however they are not able to communicate their findings".

If there were a simple scientific theory which had a whole bunch of experimental support and logically implied the existence of heaven then I would not hesitate to make the same claim about heaven.

 

[DaveC426913]

I also did not say that it is impossible to disprove the theory. That would be easy: just run an experiment whose results show causal influences being received from an infalling object past the point where the theory says no causal influences can be received. If such an experiment is ever done, GR (or at least this solution of it) will have to be revised.

Frankly I do not understand this defensive approach. Einstein's general relativity is a masterpiece and clearly very useful but that does not mean that every single iota must be correct and that those who question parts which have never been empirically verified or perhaps can never be empirically verified are automatically idiots. When we take theories as dogmas then any potential for progress stops IMHO.

PeterDonis made none of the assertions you just implied he did.

What he said (you should know, since you quoted him) was: "GR ... will have to be revised."

 

[Dale]

Q-reeus, seriously, learn to use paragraphs. Your post is incoherent.

That said, why do you want to match coordinates at the boundary? You need the potential and other physical things to match at the boundary, but you can use whatever coordinates you like for each region separately without worrying about matching.

 

[Dale]

Are there theories which match GR outside the EH, but are different inside? If so, are they as simple as GR?

 

[Passionflower]

PeterDonis made none of the assertions you just implied he did.

These comments were in a separate paragraph and applied to the whole topic not to any person in particular.

 

[PAllen]

Are there theories which match GR outside the EH, but are different inside? If so, are they as simple as GR?

Possibly one (or all!) of the main QG contenders. However, they probably agree with GR until near the true singularity.

 

[Q-reeus]

Please describe the above in reference to istotropic Schwarzschild coordinates. Coordinates have nothing to do with physical predictions. The isotropic Schwarzschild coordinates describe the same manifold, but are istotropic everywherea, at all times.

Yes there is such a beast as isotropic Schwarzschild coords - eg."Alternative (isotropic) formulations of the Schwarzschild metric" at http://en.wikipedia.org/wiki/Schwarzschild_metric, but one almost never hears of it being used. While it is true isotropy of length scale applies, it does so at the cost of imo a strange departure in dependence on potential between length scale and clock-rate as one goes from far out to nearer the source of gravity. One that does not apply between time and radial distance in standard SM coords. AS you unlike me are accomplished in the ins and outs of GR, please explain the justification and rationale for two distinct versions of SM (if there is one apart from Eddington's complaint that c was non-ispotropic in standard SM). SM is practically synonymous with the standard form, for which my entry #138 obviously refers to.

How can you possibly say that the SM has nothing to do with physical predictions? It is after all called Schwarzschild metric as often as just SC, meaning surely the coords are accurately describing a physical manifold as it relates to a coordinate observer? Are you saying that if a distant observer looking through his/her telescope surveys a ruler laid flat on the shell surface, and then placed radially upright, there will or will not be noticed a change in length - as perceived by that observer (ie, coordinate measure)? Are you also saying the clock-rate predictions of SM will or will not coincide with the physically observed redshift perceived by that same observer?

 

[Q-reeus]

Q-reeus, seriously, learn to use paragraphs. Your post is incoherent.

Well sorry if I made you work hard and I will try and do better, but I think 'incoherent' is more than a little exaggerated.

That said, why do you want to match coordinates at the boundary? You need the potential and other physical things to match at the boundary, but you can use whatever coordinates you like for each region separately without worrying about matching.

I hope you are not serious in saying that. Read my 'incoherent' entry #138 again, slowly. As per my last entry in response to PAllen, SM has, or at least is supposed to, accurately reflect the physical metric, referenced of course to coordinate measure. So is the flat Minkowski interior metric. Disagree? If not then please acknowledge the dilemma I raised is perfectly valid.

 

[Q-reeus]

Are there theories which match GR outside the EH, but are different inside? If so, are they as simple as GR?

I don't claim to have adequately grasped or surveyed anything like all the contenders out there, but I do know Yilmaz gravity allows a sensible fit for the spherical shell problem, and a welcome 'by-product' is the absense of EH's and BH's in that theory. Supporters claim it matches all the current observational successes of GR - but of course that is heatedly rejected by GR fanboys who by overwhelming weight of numbers successfully smother sensible discussion of such things outside of 'fringe' circles. Tyrrany of the majority is a fact. Maybe there's a better theory somewhere, but for my money it should at the very least start out with an isometric metric that doesn't give stupid predictions for shells.

 

[PAllen]

Yes there is such a beast as isotropic Schwarzschild coords - eg."Alternative (isotropic) formulations of the Schwarzschild metric" at http://en.wikipedia.org/wiki/Schwarzschild_metric, but one almost never hears of it being used. While it is true isotropy of length scale applies, it does so at the cost of imo a strange departure in dependence on potential between length scale and clock-rate as one goes from far out to nearer the source of gravity. One that does not apply between time and radial distance in standard SM coords. AS you unlike me are accomplished in the ins and outs of GR, please explain the justification and rationale for two distinct versions of SM (if there is one apart from Eddington's complaint that c was non-ispotropic in standard SM). SM is practically synonymous with the standard form, for which my entry #138 obviously refers to.

How can you possibly say that the SM has nothing to do with physical predictions? It is after all called Schwarzschild metric as often as just SC, meaning surely the coords are accurately describing a physical manifold as it relates to a coordinate observer? Are you saying that if a distant observer looking through his/her telescope surveys a ruler laid flat on the shell surface, and then placed radially upright, there will or will not be noticed a change in length - as perceived by that observer (ie, coordinate measure)? Are you also saying the clock-rate predictions of SM will or will not coincide with the physically observed redshift perceived by that same observer?

Coordinates are arbitrary. Metric is covariant geometric object. There is one manifold, infinite coordinate systems. Anything you think you can say about the manifold that is only true in one coordinate system is an artifact of no physical significance whatsoever.

Schwarzschild coordinates does not equal Schwarzschild geometry. You were drawing conclusions not based on the metric but only on the coordinates. Therefore your conclusions were not tied to physics.

Neither a hovering observer nor a free falling observer near the event horizon detects any local anisotropy at all.

 

[Q-reeus]

Coordinates are arbitrary. Metric is covariant geometric object. There is one manifold, infinite coordinate systems. Anything you think you can say about the manifold that is only true in one coordinate system is an artifact of no physical significance whatsoever.

Schwarzschild coordinates does not equal Schwarzschild geometry. You were drawing conclusions not based on the metric but only on the coordinates. Therefore your conclusions were not tied to physics.

Neither a hovering observer nor a free falling observer near the event horizon detects any local anisotropy at all.

Freely admitting to my having no training in GR, I nonetheless think all you have said here is not right. You for starters have pointedly not answered my questions re what a distant (coordinate) observer physically determines, and whether that is or is not accurately reflected by SM - as surely it ought to be if it is nothing more than an essentially meaningless construct. Your last sentence neatly sidesteps the issue as I see it, but here's hoping for an answer to my specific questions in #148!