Black hole matter accumulation

[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!

 

[PeterDonis]

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.

Yes, that's true. What does it have to do with the thought experiment I proposed? One could certainly have a black hole massive enough that sending, for example, a small probe, say a ton in size, falling inward towards the horizon would have a negligible effect on the spacetime curvature.

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.

Once again, I have never said GR is perfect or dogma, nor have I said that those who question the claim that there is a region of spacetime inside the event horizon are idiots. In fact, I acknowledged in at least one post that the questions being asked are legitimate questions. They also have legitimate answers, which I and others have given. I have not claimed that GR is a theory of everything. I have given cogent reasons for believing that the particular prediction under discussion, that there is a region of spacetime inside the black hole horizon, is a robust one.

 

[PAllen]

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!

What a distant observer sees is interesting, but just a matter of 'seeing'. My statement about local observations was not sidestep, but a point that in GR local physics paramount. Cosmologically, you can make good arguments for billion light year differences in distance and factors of c difference of speed for very distant objects, using different reasonable definitions.

As for #148, I won't touch it. I neither know about nor am interested in Yilmaz theories. I am interested in quantum gravity and string theoretic approaches (but have limited knowledge of them).

 

[Q-reeus]

What a distant observer sees is interesting, but just a matter of 'seeing'.

Cannot agree with that. Take the temporal component of SM. As you must well know, redshift follows directly from applying SM to the situation of emitter and receiver at differing potentials. Just 'optical illusion'? How about this thought experiment: Distant observer sends down a clock to the surface of planet X, waits a time T, and retrieves said clock. Repeats the procedure a second time, but now waits some different time T2 before retrieving as before. It is now an easy matter to subtract out any complications of the lowering and raising parts, and just figure out precisely the time dilation factor experienced by the lowered clock. Are you in agreeance or not that the so determined clock rate will have *physically* been depressed as per SM? Yes or no please! If yes, do you somehow think that the SM length measure would not have equally valid *physical* consequences, revealed by a suitable analogous procedure?

My statement about local observations was not sidestep, but a point that in GR local physics paramount.

I accept that's what you meant, but again, can't agree. Why should local physics be paramount - isn't the 'relative' part of General Relativity telling us this is at least equally about relating 'here' to 'there'? What else is SM designed for?

As for #148, I won't touch it. I neither know about nor am interested in Yilmaz theories. I am interested in quantum gravity and string theoretic approaches (but have limited knowledge of them).

My apologies for that typo - should have been #146, not #148. So feel free to comment on #146 (although a suitable response to the above would answer much of that anyway).

 

[Dale]

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.

You are right, it is an exaggeration.

I hope you are not serious in saying that.

Completely. There is never any need to match coordinates.

Read my 'incoherent' entry #138 again, slowly.

No thanks. I am not going to make more effort reading it than you made writing it.

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.

No disagreement, but what has that to do with your "dilemma"?

There is no need for different coordinate charts to be matched up to each other. There is not even a requirement that different coordinate charts cover the same region of the manifold. The only requirement for coordinate charts is that in any region of the manifold covered by two coordinate charts there needs to be a diffeomorphism between the two.

So your dilemma is a non-issue. They don't need to match up so there is no problem if they don't.

 

[PAllen]

Cannot agree with that. Take the temporal component of SM. As you must well know, redshift follows directly from applying SM to the situation of emitter and receiver at differing potentials. Just 'optical illusion'? How about this thought experiment: Distant observer sends down a clock to the surface of planet X, waits a time T, and retrieves said clock. Repeats the procedure a second time, but now waits some different time T2 before retrieving as before. It is now an easy matter to subtract out any complications of the lowering and raising parts, and just figure out precisely the time dilation factor experienced by the lowered clock. Are you in agreeance or not that the so determined clock rate will have *physically* been depressed as per SM? Yes or no please! If yes, do you somehow think that the SM length measure would not have equally valid *physical* consequences, revealed by a suitable analogous procedure?

Note that all coordinates (Kruskal, isotropic SM, whatever) agree on the result of this experiment, so it is not coordinate dependent. However, aspects of its interpretation are coordinate dependent. I will pose an argument I have with many people about 'where the missing time is in the twin paradox'? In my view, it truly has no location. The analogy I make is as follows: imagine a straight, vertical line between A and B, and also a wiggly line between A and B on a flat Euclidean plane. For the wiggly line, where is the extra length? I hope you see this is completely meaningless - I can line up the straight line with the bottom, middle, or top of the wiggly line and get whatever answer I want. I claim the twin paradox is semantically identical to this. Further, I claim, so is your example. What makes the time difference physical (invariant) is exactly the fact that the world lines of the clocks have two intersections. Then, and only then, is there an invariant statement to make: the proper time between intersections along one world line is less than the other.

I accept that's what you meant, but again, can't agree. Why should local physics be paramount - isn't the 'relative' part of General Relativity telling us this is at least equally about relating 'here' to 'there'? What else is SM designed for?

I completely disagree with your concept of GR. In my mind, it says SR concepts only apply locally to free falling frames. Further, it says global distances and 'velocity at a distance' and 'time at a distance' have no preferred definitions at all. Pick different (sensible!) ways of extending a local simultaneity globally, and get completely different answers to how far away something is. Same for each other concept.

 

[Passionflower]

Yes, that's true. What does it have to do with the thought experiment I proposed? One could certainly have a black hole massive enough that sending, for example, a small probe, say a ton in size, falling inward towards the horizon would have a negligible effect on the spacetime curvature.

OK you send that probe and then near the EH you will get almost no information from this probe because it is almost like being frozen.
Then what will you try to prove?

 

[Q-reeus]

Completely. There is never any need to match coordinates.

Really? See below.

No thanks. I am not going to make more effort reading it than you made writing it.

Disarm me with some initial civility, and then this back-hander. Good thing you don't treat other respondents with such grace.

No disagreement, but what has that to do with your "dilemma"?

There is no need for different coordinate charts to be matched up to each other.

So tears, rips, and physically implausable jumps in potential dependence are OK in GR? Confirms my worst fears.

There is not even a requirement that different coordinate charts cover the same region of the manifold.

Not sure whether that means overlap, but either way, not the issue.

The only requirement for coordinate charts is that in any region of the manifold covered by two coordinate charts there needs to be a diffeomorphism between the two.

Meaning fit them together somehow - even if it is a physically nonsensical force-fit. That IS the issue.

So your dilemma is a non-issue. They don't need to match up so there is no problem if they don't.

So you assert. But if you care to follow my #146 and #153, and then go back to #138, something should light up internally. I sure hope so.

 

[Q-reeus]

Note that all coordinates (Kruskal, isotropic SM, whatever) agree on the result of this experiment, so it is not coordinate dependent.

Of course - but we have been discussing SM - stationary observers. Why throw in irrelevant issues?

However, aspects of its interpretation are coordinate dependent. I will pose an argument I have with many people about 'where the missing time is in the twin paradox'? In my view, it truly has no location. The analogy I make is as follows: imagine a straight, vertical line between A and B, and also a wiggly line between A and B on a flat Euclidean plane. For the wiggly line, where is the extra length? I hope you see this is completely meaningless - I can line up the straight line with the bottom, middle, or top of the wiggly line and get whatever answer I want. I claim the twin paradox is semantically identical to this. Further, I claim, so is your example. What makes the time difference physical (invariant) is exactly the fact that the world lines of the clocks have two intersections. Then, and only then, is there an invariant statement to make: the proper time between intersections along one world line is less than the other.

The wiggly vs straight line and Twin Paradox stuff is obviously true but equally not relevant. I will take it from the last sentence as a grudging admission though that there are perfectly valid *physical* consequences predicted as per SM, and that this will apply to both temporal and distance measure. That being so, it gets back to my argument in #138 one can of course mathematically force-fit a union between exterior SM and interior MM, but in so doing physical reasonableness is trashed. As I said there - one has to 'magically' destroy potential dependence of at least the radial metric component, and for consistency, that should apply to the temporal component also. Which is simply screaming loudly to me at least that SM and thus EFE's are plain wrong. But shucks, laymen should know their place, hey!

I completely disagree with your concept of GR.

Well perhaps you had better spell out what you see as my concept of GR - I don't like words being put in my mouth.

In my mind, it says SR concepts only apply locally to free falling frames.

And I have been mistakenly espousing SR concepts when it should have been GR? Where exactly?

Further, it says global distances and 'velocity at a distance' and 'time at a distance' have no preferred definitions at all. Pick different (sensible!) ways of extending a local simultaneity globally, and get completely different answers to how far away something is. Same for each other concept.

So the clock retrieval example I gave you is what, a hopelessly confusing problem for GR that 'cannot be sensibly defined or evaluated'? Holy cow. Could have sworn people have been performing precise tests of redshift etc, using SM.

 

[Dale]

So tears, rips, and physically implausable jumps in potential dependence are OK in GR? Confirms my worst fears.

In GR the scalar potential is replaced by the metric tensor. It is a more general object, covering situations that don't admit a scalar potential. The metric tensor doesn't have anything that could be described as a tear, rip, or jump, in the spacetime you describe, regardless of what coordinates you use.

Meaning fit them together somehow - even if it is a physically nonsensical force-fit. That IS the issue.

It is a non-issue. Use any coordinates you like for either region. As long as there is a diffeomorphism at the border they do not need to match.

 

[Q-reeus]

In GR the scalar potential is replaced by the metric tensor. It is a more general object, covering situations that don't admit a scalar potential.

Quite aware that spinning matter etc requires extra, tensorial components to describe. But let's get it right for a simple stationary shell, shall we?

The metric tensor doesn't have anything that could be described as a tear, rip, or jump, in the spacetime you describe, regardless of what coordinates you use.

Sure, and I was using a bit of hyperbole re rip'n'tear to emphasize a point - there is a need for a physically consistent transition.

It is a non-issue. Use any coordinates you like for either region. As long as there is a diffeomorphism at the border they do not need to match.

But it can't be any old diff. I don't think you have really grasped what the main point of #138 was. There are physical and precisely defined effects as per clock example in #153 (and if you really need it, I will cook up one involving length measure specifically). So please don't repeat the mantra SM is only a 'handy but arbitrary chart'. Rubbish. It is supposed to, and in weak gravity does a very good job of, accurately predicting measurable physical effects. Period. The fact that some of those effects are not locally observable is irrelevant to the issue raised.

Paragraph break - just for Dale. So, to drive it home again, recall from #138 that temporal and radial metric components have identical functional form exterior to the shell outer surface - in regime described by SC's. Recall we have established these coords accurately account for redshift etc. Now unless you want to claim that somehow nature-as-traffic-cop strangely and radically descriminates, there is a deep consistency issue to face here.

Would you have redshift disappear via a small hop from shell exterior to interior? If not (and of course it won't), why would the functionally identical (re grav potential) radial metric component go all haywire and inexplicably jump back to the 'infinity' value? You are truly comfortable with that? Seems much, much more reasonable to me that, having a consistent potential dependence everywhere exterior to the shell, this sensibly persists within. I don't personally believe in mathematical magic, whether or not that makes me 'fringe'.
Oh my, is it really 12 hours past my bedtime - must go.:zzz:

 

[PeterDonis]

OK you send that probe and then near the EH you will get almost no information from this probe because it is almost like being frozen.
Then what will you try to prove?

I drop the probe, freely falling into the hole. The probe is pre-programmed to send a radio signal back outward towards me every 1 second, by its clock. I can then calculate that I should receive the last signal I will ever receive from the probe at a certain time according to my clock. The next signal the probe sends after that "last" signal will be sent from below the horizon, according to the theory, so it will never reach me. If, then, I run such an experiment and I receive a radio signal from the probe at any time after the time at which the theory predicts I should receive the last signal, then GR's prediction is falsified.

Of course if GR's prediction is *true*, I will wait forever and never receive another signal from the probe after the "last" one I predicted I would receive. So at any finite time interval after receiving the "last" signal, a skeptic could always say, "Yes, you haven't received another signal from the probe *yet*, but you *might* receive one at some time in the future." At that point we're talking about the problem of induction, not anything specific to GR. It's true, technically, that I will never be able to *prove* GR correct this way; but at any time, I can certainly tell without ambiguity if the data to date are still consistent with the theory.

 

[Dale]

Sure, and I was using a bit of hyperbole re rip'n'tear to emphasize a point - there is a need for a physically consistent transition.

Sure, for the metric. There is no such need for the coordinates.

But it can't be any old diff.

Yes, it can. That is one of the central features of Riemannian geometry.

There are physical and precisely defined effects as per clock example in #153 (and if you really need it, I will cook up one involving length measure specifically). So please don't repeat the mantra SM is only a 'handy but arbitrary chart'. Rubbish. It is supposed to, and in weak gravity does a very good job of, accurately predicting measurable physical effects.

Sure. So do all other coordinate systems. The measurable physical results are all tensors, so they are agreed upon by all coordinate charts. That is the whole point of writing the laws in a manifestly covariant form.

Would you have redshift disappear via a small hop from shell exterior to interior?

Of course not, the metric is continuous.

why would the functionally identical (re grav potential) radial metric component go all haywire and inexplicably jump back to the 'infinity' value?

Because you change coordinates. The continuity of the metric does not imply nor require continuity of the components of the metric as expressed in different coordinate systems.

Seems much, much more reasonable to me that, having a consistent potential dependence everywhere exterior to the shell, this sensibly persists within.

I agree. Again, the metric and the coordinates are not the same thing at all. The metric must be continuous, and every individual coordinate chart must also be continuous, but two different coordinate systems need not be continuous with each other anywhere.

 

[PeterDonis]

Would you have redshift disappear via a small hop from shell exterior to interior? If not (and of course it won't), why would the functionally identical (re grav potential) radial metric component go all haywire and inexplicably jump back to the 'infinity' value?

It doesn't. The metric inside the shell is "flat" in the sense that the metric coefficients are independent of the coordinates, so that it can be written in the Minkowski form. But the coordinates themselves are scaled differently than they are at infinity, so that what you are calling the "potential" matches up across the thin spherical shell, and the length contraction and time dilation factors do too.

Remember also that an "infinitely thin" spherical shell is unphysical if it has nonzero mass; there has to be *some* region of finite thickness where the stress-energy tensor is nonzero, and in that region the metric coefficients will change too.

 

[Passionflower]

I drop the probe, freely falling into the hole. The probe is pre-programmed to send a radio signal back outward towards me every 1 second, by its clock. I can then calculate that I should receive the last signal I will ever receive from the probe at a certain time according to my clock. The next signal the probe sends after that "last" signal will be sent from below the horizon, according to the theory, so it will never reach me. If, then, I run such an experiment and I receive a radio signal from the probe at any time after the time at which the theory predicts I should receive the last signal, then GR's prediction is falsified.

Yes but that is not what we are talking about right? Aren't we are talking about proving it passes the horizon into another region?

I do not believe anybody here in this topic questions the Sch. solution up to the EH. The question is what happens beyond the EH if anything at all. I do not understand how your experiment will prove anything related to that.

Making all kinds of general statements what happens beyond the EH is no longer science IMHO, we might as well claim that beyond the EH are stacked turtles. We cannot possibly know anything about it.

You could say "well we could in theory send someone" but what does that prove as the information from him dries up as soon as he is close to the EH. We simply cannot experimentally verify he crossed the EH.

I like Popper's idea about theories or parts of theories that cannot be falsified.

 

[PeterDonis]

I like Popper's idea about theories or parts of theories that cannot be falsified.

Um...I just described how the standard GR theory about a black hole spacetime can be falsified. I gave the exact experimental result that would do it. What more do you want?

Yes but that is not what we are talking about right? Aren't
we are talking about proving it passes the horizon into another region?

I'm confused. Are we talking about proof, or are we talking about falsification? I have not claimed I can *prove* the standard GR theory to be correct. In fact I have said explicitly that scientific theories can't be "proved" (though, as I noted just now, they can be falsified).

We can, however, gather indirect evidence and make cogent arguments that bear on the question. For example, we can in principle measure and report out to "infinity" the curvature components all the way down to just a smidgen above the horizon, and verify that they match the GR prediction. We can also observe objects traveling on infalling worldlines all the way to the horizon and see that their trajectories match the GR prediction. We can also, of course, observe that nothing ever comes *out* of the horizon. Further, we can take the limit of our measurements to calculate values for physical quantities *at* the horizon, and verify that, as GR predicts, they are finite and nonsingular.

At that point, as I've said before, we are faced with two choices:

(1) We can believe that, since physical objects have gone *into* the horizon, and none have come out, and there is no physical reason for them to have ceased to exist *at* the horizon, there must be a region of spacetime inside the horizon, where those objects went; or

(2) We can believe that somehow, spacetime just "stops" at the horizon, and all those objects we saw fall into it just stopped existing when they hit the horizon, even though there is no physical reason for them to have done so.

By taking option (1), are we adopting a belief about a region of spacetime that we can never directly observe? Yes, certainly. But, IMHO, it is better than the alternative--adopting a belief that, in order to avoid having to believe in a region of spacetime we can't directly observe, forces us to believe that physics all of a sudden starts working completely differently at the horizon, for no apparent reason.

 

[Passionflower]

We can, however, gather indirect evidence and make cogent arguments that bear on the question. For example, we can in principle measure and report out to "infinity" the curvature components all the way down to just a smidgen above the horizon, and verify that they match the GR prediction.

OK, I am with you here.

We can also observe objects traveling on infalling worldlines all the way to the horizon and see that their trajectories match the GR prediction.

Again, alright.

We can also, of course, observe that nothing ever comes *out* of the horizon.

Yes, correct.

Further, we can take the limit of our measurements to calculate values for physical quantities *at* the horizon, and verify that, as GR predicts, they are finite and nonsingular.

Sure we can calculate, but calculations and experiment are different things right?

At that point, as I've said before, we are faced with two choices:
(1) We can believe that, since physical objects have gone *into* the horizon,...

Ooops, they have gone into the horizon? All I think we can observe is that they freeze arbitrarily close to the horizon.

(2) We can believe that somehow, spacetime just "stops" at the horizon, and all those objects we saw fall into it just stopped existing when they hit the horizon, even though there is no physical reason for them to have done so.

I think there are more options, I am not saying these options are true but since you ask the most obvious other option is:

(3) Everything arbitrarily close to the EH is simply frozen and does not move, they are simply stuck there.

Now I am aware that the Sch. solution does not state that but so what? We are talking about empirical verification here not theory right?

Even if we would have a way of knowing something passes the EH then still we do not know what is beyond. Yes, we can calculate it using the Sch. solutions, calculations I do all the time and they work fine. But again we are talking here about experiment not theory.

 

[PeterDonis]

Sure we can calculate, but calculations and experiment are different things right?

Yes, but the calculation of a limiting case which is just a smidgen beyond the last point we can experimentally measure and send the results back to infinity is pretty close to a direct experimental result. We make these sorts of extrapolations all the time in physics and nobody bats an eye; maybe the results aren't exact but they're pretty close. So for this method to suddenly become egregiously wrong just because we're close to a black hole horizon--even though, as you know, locally you can't tell such a place from any other place in spacetime--physics would have to suddenly start working completely differently, for no apparent reason.

There are more options, I am not saying these are the case but since you ask the mos obvious option is:

(3) Everything arbitrarily close to the EH is simply frozen and does not move.

Technically you are right, this is a different alternative than (2), but in practice it works out the same. Remember that, as you know and have posted in other threads, the infalling observer himself does not see his own clock freezing; he will measure a finite amount of proper time from a given finite radius above the horizon, to the horizon. And then what happens? Saying that he actually "freezes" at that point (instead of the freezing being an illusion as seen by the observer far away, because of the delay in light getting out) is, practically speaking, the same as saying he ceases to exist; it's saying that physics suddenly starts working completely differently, for no apparent reason.

 

[Passionflower]

Yes, but the calculation of a limiting case which is just a smidgen beyond the last point we can experimentally measure and send the results back to infinity is pretty close to a direct experimental result. We make these sorts of extrapolations all the time in physics and nobody bats an eye; maybe the results aren't exact but they're pretty close. So for this method to suddenly become egregiously wrong just because we're close to a black hole horizon--even though, as you know, locally you can't tell such a place from any other place in spacetime--physics would have to suddenly start working completely differently, for no apparent reason.

Yes, OK, I think these are some solid arguments!

Remember that, as you know and have posted in other threads, the infalling observer himself does not see his own clock freezing;

Correct.

he will measure a finite amount of proper time from a given finite radius above the horizon, to the horizon.

Yes we can calculate that using the Sch. solution but do not know that is the case empirically? To the horizon or slightly above the horizon?

Remember, as you undoubtedly know, we cannot even empirically verify the correctness of the Sch. solution. For instance Pound-Rebka does not measure the discrepancy between delta r and delta rho as we simply lack the accuracy in instrumentation.

 

[PeterDonis]

Yes we can calculate that using the Sch. solution but do not know that is the case empirically? To the horizon or slightly above the horizon?

Remember, as you undoubtedly know, we cannot even empirically verify the correctness of the Sch. solution. For instance Pound-Rebka does not measure the discrepancy between delta r and delta rho as we simply lack the accuracy in instrumentation.

We do today, yes, but our instrumentation continues to get more accurate. I have no problem imagining that we will be able to detect the spatial as well as the temporal effects of spacetime curvature around the Earth in the future. Similarly, I have no problem imagining that at some future time we will be able to drop probes towards black holes, after synchronizing their clocks with ours at some reasonably large radius, and have the probes send back time-stamped radio signals that confirm the GR calculation of proper time elapsed in falling to the horizon.

 

[PAllen]

Of course - but we have been discussing SM - stationary observers. Why throw in irrelevant issues?

Because, at times, you have been treating one set of coordinates as specially meaningful. Some features you complain about don't exist in other coordinates. Therefore they are coordinate artifacts, not physical predictions.

The wiggly vs straight line and Twin Paradox stuff is obviously true but equally not relevant. I will take it from the last sentence as a grudging admission though that there are perfectly valid *physical* consequences predicted as per SM, and that this will apply to both temporal and distance measure. That being so, it gets back to my argument in #138 one can of course mathematically force-fit a union between exterior SM and interior MM, but in so doing physical reasonableness is trashed. As I said there - one has to 'magically' destroy potential dependence of at least the radial metric component, and for consistency, that should apply to the temporal component also. Which is simply screaming loudly to me at least that SM and thus EFE's are plain wrong. But shucks, laymen should know their place, hey!

The point of the wiggly line analogy was to emphasize the difference between physical predictions versus coordinate values. However you want to construct the clock paths, I could come up with coordinates that say the clock that shows more time at the end, for example, matched the other clock for 99% of the the time on this other clock; then, shot forward only as the lower clock was brought up. I will agree those would be strained coordinates, but the point is, it is only the comparison at the end that is a true physical prediction.

Well perhaps you had better spell out what you see as my concept of GR - I don't like words being put in my mouth.

In several places you talk about an observer making physical statements about what is true at a distance. In SR, this can be made to work because there exist global frames for inertial observers. In GR all such statements have no unique validity.

And I have been mistakenly espousing SR concepts when it should have been GR? Where exactly?

So the clock retrieval example I gave you is what, a hopelessly confusing problem for GR that 'cannot be sensibly defined or evaluated'? Holy cow. Could have sworn people have been performing precise tests of redshift etc, using SM.

No, it is trivial and can be computed in any coordinates.

As to your so call main problem, I just don't see the problem. The total solution for a shell is simply the Schwarzschild geometry outside, a non vacuum solution through the shell, and Minkowski inside. There would be no discontinuities. If the shell were transparent, and and light were emitted inside the shell of some frequency observed locally, it would red shifted when received by an outside observer slightly more than a similar signal from the surface of the shell (the difference being due to shell). Despite their being no formal, general, potential in GR, this experiment would behave very similar to the Newtonian case. Almost all of these properties follow directly from Birkhoff's Theorem, which is rigorously proven for GR.

 

[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.

This is a truly fundamental misunderstanding. The isotropic coordinates are just different coordinates for the same geometry, as are the Kruskal, Eddington, Gullestrand, etc. They all represent the same metric as a geometric object, they all make the same physical predictions. It is no different that polar versus rectilinear versus logarithmic coordinates on a plan. Does drawing different lines on a plane change its geometry? No. However, the Euclidean metric expression can only be used with rectilinear coordinates. Using the standard tensor transformation law, you would derive different metric expressions for the other coordinates that would yield all the same geometric facts.

 

[Passionflower]

We do today, yes, but our instrumentation continues to get more accurate. I have no problem imagining that we will be able to detect the spatial as well as the temporal effects of spacetime curvature around the Earth in the future.

I have no problem with that either.

Similarly, I have no problem imagining that at some future time we will be able to drop probes towards black holes, after synchronizing their clocks with ours at some reasonably large radius, and have the probes send back time-stamped radio signals that confirm the GR calculation of proper time elapsed in falling to the horizon.

Well, I am hand waving but I think I see some potential problems, mainly to do with light travel time issues.

It would be nice to start a topic were we calculate stuff. Care to start one perhaps we can see people actually put down calculations and formulas? Should be relatively simply, a prove fall from zero and then some light travel times to the observer at a large r receiving signals.

It is unfortunate we have so many learned folks here who think they are experts (and some indeed are) but when it comes to showing numbers or formulas they are typically not around.

 

[Passionflower]

This is a truly fundamental misunderstanding. The isotropic coordinates are just different coordinates for the same geometry, as are the Kruskal, Eddington, Gullestrand, etc. They all represent the same metric as a geometric object, they all make the same physical predictions. It is no different that polar versus rectilinear versus logarithmic coordinates on a plan. Does drawing different lines on a plane change its geometry? No. However, the Euclidean metric expression can only be used with rectilinear coordinates. Using the standard tensor transformation law, you would derive different metric expressions for the other coordinates that would yield all the same geometric facts.

PAllen is correct here, different coordinates are like different fishnet stockings on a woman's leg, the leg does not change!

 

[PAllen]

I note that no one has commented on the ideas in my post #128, that these unverifiable issues become verifiable if there are exceptions to cosmic censorship; and there is plausible evidence that there may be exceptions.

 

[atyy]

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

You may like to read these discussions http://books.google.com/books?id=ZN...f+space+and+time+solvay&source=gbs_navlinks_s (just type in "cosmic censorship" in the seach box).