Black hole matter accumulation

[DaveC426913]

Could you clarify how long it would take for this to happen? In other words, I think I am reading that all the posters on this thread agree that to the outside universe, time goes very slowly (maybe even stops) at the EH. This applies to this falling towards the BH, so I assume it applies to things going out again. So the rest of the universe is sitting on our hovering spaceships and watching the Hawking radiation coming out past the EH. But how does it get out? The rest of the universe is long gone by the time this radiation manages the trip.

It's the same argument as things falling into the BH. Sure, the proper time on the falling object proceeds at the normal rate (whatever that is). But the rest of the universe outside the EH has lived out it's lifetime and no longer exists by the time the falling observer crosses the EH. All of the Hawking radiation will be frozen at the EH going the other way, just as all of the falling objects will be frozen at the EH. The BH will never lose any mass, as view by those of us who are in the rest of the universe, it will only exponentially gain mass until it consumes everything.

I see your point. Virtual particle production occurs microscopically close to the EH. Events there should be stretched out over the age of the universe as observed by a distant observer.

It's part right and part wrong.

EM travels at the speed of light, so it will always climb out of the gravity well at a speed of c, so no weirdness there. But what the time dilation does do though is red-shift the EM. Essentially Hawking radiation will be red-shifted to virtually zero.

 

[PeterDonis]

Our judgment what to consider good or bad coordinate system is different. The same about which observer should be chosen for global bookkeeping either distant observer that is not going to fall into particular black hole or the one that is falling towards particular black hole.

It's not a question of whether particular coordinates are "good" or "bad". It's a question of whether or not a particular coordinate chart covers the whole spacetime, or only a part of it. That's not a matter of opinion, it's a matter of math. The exterior Schwarzschild chart only covers the region of spacetime outside the horizon. The other charts I mentioned all cover both that region *and* the region inside the horizon.

Obviously, if you're talking about a region of spacetime covered by multiple coordinate charts, you can pick whichever chart you want to to describe the physics. So as long as you're talking about events that happen outside the horizon, yes, you can choose the exterior Schwarzschild chart for "global bookkeeping". But as soon as you try to talk about what happens at or inside the horizon, you can no longer make that choice, because the chart simply doesn't cover that region.

If you want to argue that the region inside the horizon does not exist, you can try, but you can't do it using things that are particular to one coordinate system. You have to look at covariant objects (like vectors or tensors) and invariant objects (like scalars). Schwarzschild coordinate time is not such an object. The proper time along a particular timelike worldline between two particular events is. So is the curvature tensor; so are the null vectors that define the light cone at a particular event, such as the event where a particular timelike observer crosses the horizon. And so is that observer's 4-velocity vector at that same event. So when I say that there are timelike worldlines that reach the horizon and must still be going inward there, I'm talking entirely in terms of covariant and invariant objects.

But ingoing side of light cone continues inwards? Basically you are saying that light can cross EH and therefore massive object can do that as well.
Then the question is - why do you think that light can cross EH?

For the same reason I think a timelike object can cross the horizon: there are ingoing null worldlines that reach the horizon and are still going inward there, and the curvature there is finite so those worldlines can't just stop and cease to exist.

You can compute that the curvature is finite at the horizon in Schwarzschild coordinates?
How is that?

It's a standard computation that's given in all the major GR textbooks I'm aware of. I can't seem to find a good online link showing it, but it's straightforward if tedious; I can post an outline of it if you're really interested, but that will take some time. The only technical point about using exterior Schwarzschild coordinates is that you have to take a limit as r -> 2M, since the metric is singular at r = 2M. But the formulas for the Riemann tensor components are all non-singular at r = 2M, so the bit about taking a limit, as far as I can see, is only really necessary to satisfy mathematical purists.

Of course, you could also use any of the other coordinate systems I mentioned, which are not singular at r = 2M, and then you wouldn't even have to take a limit. Since the curvature is a covariant tensor, if it is finite in one coordinate system is is finite in any coordinate system. (You can compute scalar curvature invariants as well, which are the same in all coordinate systems, and are finite at the horizon.) So even if the computation could not be done in Schwarzschild coordinates, it wouldn't matter; it could still be done.

And still you haven't answered my question - why do you think that infinite curvature and break in the continuity of spacetime are physical things?

I haven't answered it because it's irrelevant to the question of whether objects can reach and cross the horizon. Curvature only becomes infinite at the singularity at r = 0.

If you insist on an answer even though it's irrelevant to the EH question, I'm not sure that infinite curvature is an actual physical thing. It might well be an indication that classical GR cannot properly describe what happens at r = 0 inside a black hole. We may need a theory of quantum gravity to do that. But, as I said, that's irrelevant to the question of whether objects can reach and cross the horizon, since the curvature is finite there (and can be arbitrarily small if the hole's mass is large enough).

 

[Passionflower]

The Schwarzschild r coordinate is actually a measure of curvature, just take 1/r to get the curvature. Clearly at the EH it is finite while at r->0 it goes to infinity.

Does the region passed the event horizon exist?
It certainly does not exist for outside observers, only observers who pass the EH will be able to experience this region.

 

[PeterDonis]

The Schwarzschild r coordinate is actually a measure of curvature, just take 1/r to get the curvature.

Actually, IIRC, the components of the Riemann tensor in Schwarzschild spacetime go as 1/r^3. According to Wikipedia (and their formula matches what I remember from MTW, anyway), at least one curvature invariant, the Kretschmann invariant, goes as 1/r^6.

http://en.wikipedia.org/wiki/Schwarzschild_metric

 

[PeterDonis]

Does the region passed the event horizon exist?
It certainly does not exist for outside observers, only observers who pass the EH will be able to experience this region.

By "exist" I meant "is part of the spacetime as a whole", which is true. I don't like using words like "exist" to refer to things which are observer-dependent, which is why I don't like the sense of "exist" in which the region inside the horizon can "exist" for infalling observers but not for observers far away. But that's just my preference. If necessary, we can describe everything that goes on without using the word "exist" at all.

 

[?????]

I wonder about gravity itself being time dependent. For example, the notion that gravity waves are spreading through the universe at the speed of light is the basis for the LIGO experiment having been underway for many years now and costing a great deal of money. This idea means that gravity is "traveling" , so to speak, outward away from the gravitating bodies (e.g. two massive planets caught in each others orbit and spinning as a pair).

So, how does gravity get past this frozen time shell surrounding a black hole? If light is red shifted to zero at the EH, then what happens to gravity going outward on the same trip. Shouldn't the apparent gravitational pull of the black hole mass appear to be zero to the rest of the universe outside the EH?

 

[ZapperZ]

I wonder about gravity itself being time dependent. For example, the notion that gravity waves are spreading through the universe at the speed of light is the basis for the LIGO experiment having been underway for many years now and costing a great deal of money. This idea means that gravity is "traveling" , so to speak, outward away from the gravitating bodies (e.g. two massive planets caught in each others orbit and spinning as a pair).

Why is this odd? Take a charge particle under electrostatic situation. It has a static E-field everywhere. Now jiggle it up and down. How fast do you think the disturbance in the E-field propagate?

So why is this any different than gravity?

Zz.

 

[Drakkith]

I wonder about gravity itself being time dependent. For example, the notion that gravity waves are spreading through the universe at the speed of light is the basis for the LIGO experiment having been underway for many years now and costing a great deal of money. This idea means that gravity is "traveling" , so to speak, outward away from the gravitating bodies (e.g. two massive planets caught in each others orbit and spinning as a pair).

So, how does gravity get past this frozen time shell surrounding a black hole? If light is red shifted to zero at the EH, then what happens to gravity going outward on the same trip. Shouldn't the apparent gravitational pull of the black hole mass appear to be zero to the rest of the universe outside the EH?

If you view gravity as a curvature of spacetime then there is no need for it to "escape" the black hole. Imagine the bowling ball on a trampoline example. If gravity is simply that curved surface then it is immediately obvious why gravity can escape, as it is curvature of spacetime.

 

[PeterDonis]

So, how does gravity get past this frozen time shell surrounding a black hole?

For a good short answer to this, see the Usenet Physics FAQ entry on "how does gravity get out of a black hole?" at:

http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/black_gravity.html

Key quote:

If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole.

In other words, the gravity you feel as a "pull" towards the black hole is actually "propagating" from the past, from the object that originally formed the hole.

It's also important to draw a distinction between the gravity waves propagating from a time-dependent system, such as a binary pulsar, and the "gravity" of a static system such as a black hole. The latter type of gravity doesn't "propagate" in quite the same way as the former.

 

[?????]

For a good short answer to this, see the Usenet Physics FAQ entry on "how does gravity get out of a black hole?" at:

http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/black_gravity.html

I looked at this link and do not find its reasoning to be compelling.

I cannot think of a single other instance where a scientific enterprise is so critically dependent on a mathematical model with featuring a singularity (the Schwarzschild radius). In my view, forming a theory around this undefinable mathematical region is beyond belief. The singularity issue trumps all other mathematical reasoning.

I feel reinforced in this belief by reading the very discussions going on in this thread. The posters here are obviously very informed in the technology, very dedicated and very intelligent - yet the large disparities in viewpoints seems beyond reconciliation, despite the fact that all involved can refer to the same Schwarzschild mathematical model to back up their viewpoint - and have done so repeatedly in this thread with conviction. That is the problem with singularities - since you can't define with certainty what is happening, anything can be happening. And the theories presented in this thread about what happens after the EH cover the gamut of possibilities, all with supposed mathematical justification. When a theory is so complex that nobody can truly understand it, then anyone can come up with a theory to explain it.

The singularity at the Schwarzschild radius is the starting point in the confusion by keepit (who began this thread) and by others, especially in the more adept posters I have referred to. The Schwarzschild Metric is the key mathematical starting point for all this confusion. This defines, by default, that it cannot possibly be correct.

 

[DaveC426913]

The singularity at the Schwarzschild radius is the starting point in the confusion by keepit (who began this thread) and by others, especially in the more adept posters I have referred to. The Schwarzschild Metric is the key mathematical starting point for all this confusion. This defines, by default, that it cannot possibly be correct.

Because we here on PF do not agree, this is enough for you to conclude that it cannot possibly be correct?

 

[PeterDonis]

I looked at this link and do not find its reasoning to be compelling.

Why not? The rest of your post talks about coordinate singularities, but there's nothing at the page I linked to about coordinate singularities; it doesn't even talk about coordinate systems at all. The discussion is entirely in terms of coordinate-free (covariant or invariant) concepts.

That said, let's talk about the "singularity" itself:

I cannot think of a single other instance where a scientific enterprise is so critically dependent on a mathematical model with featuring a singularity (the Schwarzschild radius). In my view, forming a theory around this undefinable mathematical region is beyond belief. The singularity issue trumps all other mathematical reasoning.

The theory is not "formed around" the coordinate singularity at the Schwarzschild radius. Nor does the mathematical model depend on it. See below for more comments on that.

But even if we restrict attention to Schwarzschild coordinates and the coordinate singularity they have at r = 2M, you're making an awfully big deal about something which is not even a physical concept at all, just a mathematical artifact of a particular coordinate system. Coordinate singularities are well-understood and not at all mysterious. Our standard system of locating points on Earth by latitude and longitude has a coordinate singularity--actually two of them, at the North and South poles. See, for example, the Wiki page here:

http://en.wikipedia.org/wiki/Mathematical_singularity#Coordinate_singularities

Does that mean the North and South poles are somehow mysterious, or that there is some problem with "forming a theory of Earthbound locations" using latitude and longitude?

I feel reinforced in this belief by reading the very discussions going on in this thread. The posters here are obviously very informed in the technology, very dedicated and very intelligent - yet the large disparities in viewpoints seems beyond reconciliation, despite the fact that all involved can refer to the same Schwarzschild mathematical model to back up their viewpoint - and have done so repeatedly in this thread with conviction.

You are mistaken. Some people have indeed referred to Schwarzschild coordinates to back up their views; others, such as I, have said that if you want to talk about the actual physics, you have to look at things that are covariant or invariant--i.e., that *don't* depend on a particular coordinate system being used. They *do* depend on the *geometry*, which is a mathematical object in its own right, independent of whatever coordinate chart or charts we use to describe it. But claims about a particular feature specific to Schwarzschild coordinates, whether it's a singularity at r = 2M or anything else, can't be used to make claims about the geometry.

So the different "viewpoints", as you call them, are due to the fact that people are talking about different things. Some are talking about a specific coordinate chart; others are talking about a geometry, independent of any particular coordinate chart, because it's the geometry that affects the physics. See below.

That is the problem with singularities - since you can't define with certainty what is happening, anything can be happening.

Really? So because the North and South poles don't have a well-defined longitude, anything can happen there?

This is a prime example of confusing coordinates with physics. The geometry of the Earth's surface is perfectly well-defined at the poles. It's just that latitude and longitude coordinates don't do a good job of describing it there. So we use other coordinates; for example, there are various "polar projections" that are used, as described here:

http://www.geowebguru.com/articles/242-polar-maps-and-projections-part-1-overview

Similarly, the geometry of the spacetime surrounding a black hole is perfectly well-defined at the event horizon; we can tell that by computing covariant and invariant quantities like the curvature tensor and showing that they are finite and well-behaved. It's just that Schwarzschild coordinates don't do a good job of describing the geometry at r = 2M. So if we want to describe things in terms of coordinates at r = 2M, we use other coordinates. There are a number of choices, which have been mentioned in this thread.

And the theories presented in this thread about what happens after the EH cover the gamut of possibilities, all with supposed mathematical justification.

As far as the "theories" presented in this thread, I don't see a gamut of possibilities; I see only two:

(1) Objects can reach and go inside the event horizon; i.e., there is a region of spacetime inside the horizon;

(2) Objects cannot reach or go inside the horizon; i.e., spacetime "ends" at the horizon, there is no region of spacetime inside it.

Theory #1 is based on looking at covariant and invariant quantities like the curvature tensor; theory #2 is based on looking at the coordinate singularity in the Schwarzschild exterior chart. So the different "theories" are because people are talking about different things.

When a theory is so complex that nobody can truly understand it, then anyone can come up with a theory to explain it.

What evidence do you have that nobody can understand GR's description of a black hole spacetime at and around the event horizon? You may have evidence that *some* people don't understand it (and you hardly need this thread to show that; there are plenty of others, not to mention plenty of other websites). But it's a long, long haul from that to the claim that *nobody* understands. If you really want to defend the latter claim, you'll need some really impressive evidence.

The singularity at the Schwarzschild radius is the starting point in the confusion by keepit (who began this thread)...The Schwarzschild Metric is the key mathematical starting point for all this confusion. This defines, by default, that it cannot possibly be correct.

No, it means that it can't describe the geometry at r = 2M. But it does just fine at describing it for r values much larger than 2M, and it even does a passable job describing it wherever r > 2M if you remember to allow for the "distortion" it introduces close to the horizon.

 

[zonde]

It's not a question of whether particular coordinates are "good" or "bad". It's a question of whether or not a particular coordinate chart covers the whole spacetime, or only a part of it. That's not a matter of opinion, it's a matter of math. The exterior Schwarzschild chart only covers the region of spacetime outside the horizon. The other charts I mentioned all cover both that region *and* the region inside the horizon.

Fine, you explained your position about what are good and bad coordinate charts.
Let me explain my position.
Good coordinate chart does not contain empirically meaningless regions of spacetime i.e. it does not make untestable pseidoscientific implications.
If coordinate chart breaks down at some point we simply say that it's domain of applicability ends there. Beyond that point live dragons.

Obviously, if you're talking about a region of spacetime covered by multiple coordinate charts, you can pick whichever chart you want to to describe the physics. So as long as you're talking about events that happen outside the horizon, yes, you can choose the exterior Schwarzschild chart for "global bookkeeping". But as soon as you try to talk about what happens at or inside the horizon, you can no longer make that choice, because the chart simply doesn't cover that region.

If you want to argue that the region inside the horizon does not exist, you can try, but you can't do it using things that are particular to one coordinate system. You have to look at covariant objects (like vectors or tensors) and invariant objects (like scalars). Schwarzschild coordinate time is not such an object. The proper time along a particular timelike worldline between two particular events is. So is the curvature tensor; so are the null vectors that define the light cone at a particular event, such as the event where a particular timelike observer crosses the horizon. And so is that observer's 4-velocity vector at that same event. So when I say that there are timelike worldlines that reach the horizon and must still be going inward there, I'm talking entirely in terms of covariant and invariant objects.

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 and both interior descriptions are contradictory.
Could I argue in this case that region inside the horizon does not exist?

For the same reason I think a timelike object can cross the horizon: there are ingoing null worldlines that reach the horizon and are still going inward there, and the curvature there is finite so those worldlines can't just stop and cease to exist.

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

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

It's a standard computation that's given in all the major GR textbooks I'm aware of. I can't seem to find a good online link showing it, but it's straightforward if tedious; I can post an outline of it if you're really interested, but that will take some time. The only technical point about using exterior Schwarzschild coordinates is that you have to take a limit as r -> 2M, since the metric is singular at r = 2M. But the formulas for the Riemann tensor components are all non-singular at r = 2M, so the bit about taking a limit, as far as I can see, is only really necessary to satisfy mathematical purists.

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.

 

[zonde]

The singularity at the Schwarzschild radius is the starting point in the confusion by keepit (who began this thread) and by others, especially in the more adept posters I have referred to. The Schwarzschild Metric is the key mathematical starting point for all this confusion. This defines, by default, that it cannot possibly be correct.

From empirical point of view there are no correct theories. That does not mean that they are useless.
We just use simple elegant theoretical constructs as a baseline for interpretation of observed facts and to analyze possible success of our future actions.
For well established theories we just know their domain of applicability and do not try to apply them where they give poor results. Lengthy discussions around Schwarzschild Metric might indicate that there is no consensus yet about it's domain of applicability.

 

[?????]

I can agree with much of what is said above, including some criticism of the view that I expressed.

But consider the implications of the link http://www.desy.de/user/projects/Phy...k_gravity.html that I commented about. 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.

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.

 

[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.