crossing the event horizon of a black hole


by MasterD
Tags: black, event, hole, horizon
aranoff
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Aug25-08, 07:41 AM
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There has been confusion about the topic of the supposed inside of a black hole (BH) in general relativity (GR). I wish to clarify this properly, rather than write small pieces in response to comments.

GR is a valid theory. It has a consistent mathematical framework, and has been verified observationally. No theory is perfect, which can be proven using Gödel's arguments. Physicists try to deal with the imperfections by imagining extensions to GR, and then calculating results. This is a proper approach to advancing physics. However, we must not confuse these extensions with the theory of GR itself. My arguments refer to GR only.

I will prove the following theorem three ways. Theorem: There is no solution of GR inside the BH.

One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.

The counterarguments do not seem clear and logical to me. For example, some of you said that it is okay to have a solution that is not valid everywhere. This contradicts the basic philosophy of boundary conditions (BC). The BC at one point determine which solutions are valid. Same for the BH. The condition at the center determines that this solution is not valid.

Two. Physical concepts must be capable of being observed in principle. If one individual can observe something, but no one else can, then the concept does not exist in physics. No observer can see something falling into the inside of the BH. Therefore, the inside does not exist.

Maybe a future theory including QM will permit the observation of the inside. This is irrelevant to my argument. I am discussing GR, not QM. In GR, the inside cannot be observed.

Some of you tried to say that although outside observers cannot see the inside of the BH, the observer falling down does see this inside. This is like saying Heaven exists. No one has observed Heaven, except for the person who died. The basic philosophy of physics is to reject ideas that people cannot observe.

Three. Okay, I gave one proof based upon mathematics, and a second based upon the philosophy of physics. I will now give a proof based upon contradiction. Normally these types of proofs are difficult for students.

Let us assume the solution exists inside the BH. Consider the simple case of a BH with zero angular momentum. Let the observer have 0 angular momentum as he falls in. Consider a time when the observer is ¼ of the way down. Let the BH be at state A at this time. At a later time, the observer is ½ of the way down. Let the BH be at state B at this time. Since the observer is at different points on the path, state A is not equal to state B.

A BH has the property that its state depends only on its mass, angular momentum, and charge. Both state A and state B have the same mass, etc. Therefore, state A is identical to state B. This contradicts the previous statement, state A is unequal to B. This proves no solution exists.
JesseM
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Aug25-08, 09:24 AM
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Quote Quote by aranoff View Post
One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.
Once again, you are using the word "solution" in a vague and slippery way which does not correspond to how it is used by physicists. There is no separate "solution" for inside the event horizon and outside, if your own invented rule was really "throw out all GR solutions involving singularities" then you should throw out the whole thing, including the region outside the event horizon. If you're going to divide up a single GR solution into two pieces, there is nothing special or magical about the event horizon, it's just a distance which has the interesting physical property of it becoming impossible for light to escape; logically, you could equally well divide the Schwarzschild solution into "the region from R=0 to R=0.5" and "the region from R=0.5 to R=infinity" (i.e. one part from the singularity up to half the distance to the event horizon in Schwarzschild coordinates, another part from half the distance to the event horizon out to infinity), and throw out the first part while saying the second part is valid. You have not made any logical connection between your poorly-defined notion of a "solution" and your arguments about the inside of the event being unobservable to outsiders, you're just using an arbitrary sort of free-association to justify dividing up a single GR solution into two pieces this way.

The other point is that you provide no coherent physical justification for throwing out solutions with singularities, just some weird pseudophilosophical statement that singularities violating the "philosopophy of boundary conditions" What is this "philosophy" exactly? Who says quantities can't go to infinity on boundaries? Physicists do tend to see infinities as a sign the theory is probably going wrong (although plenty of physicists have discussed the possibility that GR singularities could be real physical infinities), but they have physical arguments for just how far from the singularities they expect the theory can't be trusted, not made-up philosophical rules where if the theory gives bad predictions in a specific region the theory's predictions about other areas far from that region must automatically be disqualified.

Do you have any understanding of how past theories of physics such as Newtonian mechanics or classical electromagnetism have been show to "break down" in specific domains, and been shown to be approximations to some other more correct theory which can deal with these domains? In these cases it has always been that the predictions of the first theory and the second, more accurate, theory have been shown to continuously diverge as some parameter or parameters are varied so we get farther into the domain where the first theory "breaks down", like increasing the relative velocities of particles in Newtonian mechanics closer to the speed of light, or considering blackbody wavelengths closer to the ultraviolet catastrophe in classical electromagnetism (the more correct theories to deal with these situations are special relativity and quantum theory, respectively). Physicists assume that something similar will be true of GR vs. quantum gravity, and they have physical arguments for believing the divergence between the two theories will only become significant near the Planck scale. They don't just make up arbitrary rules to make things simpler for themselves, like "let's divide the Schwarzschild solution into two regions, one inside the horizon and one outside, and say that GR is valid outside but the inside contains a singularity so let's assume it's totally invalid anywhere inside".
Quote Quote by aranoff
Two. Physical concepts must be capable of being observed in principle. If one individual can observe something, but no one else can, then the concept does not exist in physics. No observer can see something falling into the inside of the BH. Therefore, the inside does not exist.
Any observer or community of observers who falls in after the object can see it cross the event horizon. What's more, in a universe with expanding space there will be regions of ordinary space (no black holes involved) which are in principle impossible to observe simply because the expansion of space between us and them carries them away from us faster than even a light signal sent from our position could ever catch up with them. Do you therefore conclude that nothing beyond a certain sphere centered on the Earth really "exists"? This would be a strangely solipsistic cosmology, with observers on different planets each concluding that nothing beyond the same-sized sphere centered on themselves really exists!
Quote Quote by aranoff
Three. Okay, I gave one proof based upon mathematics
You obviously don't understand what a "proof" is, it's not a string of poorly-connected statements based on ill-defined terms (as I said, you use 'solution' in a way that clearly doesn't correspond to the way this term is used in GR, and you fail to provide any logical connection between your argument about event horizons and your notion that we should treat the region inside the event horizon as a different 'solution' and throw it out completely).
Quote Quote by aranoff
Let us assume the solution exists inside the BH.
Again, why the arbitrary choice of dividing up the solution into "inside the event horizon" and "outside the event horizon"? Why not "inside a sphere with a radius equal to half the radius of the event horizon" and "outside that sphere", for example?
Quote Quote by aranoff
Consider the simple case of a BH with zero angular momentum. Let the observer have 0 angular momentum as he falls in. Consider a time when the observer is ¼ of the way down. Let the BH be at state A at this time. At a later time, the observer is ½ of the way down. Let the BH be at state B at this time. Since the observer is at different points on the path, state A is not equal to state B.

A BH has the property that its state depends only on its mass, angular momentum, and charge. Both state A and state B have the same mass, etc. Therefore, state A is identical to state B. This contradicts the previous statement, state A is unequal to B. This proves no solution exists.
Uh, a systems can be in the same "state" at different coordinate times, "state" just refers to the numerical values of a certain set of physical properties, if the object has identical properties at times t1 and t2 it was in the same state at both times, you can't use the fact that t1 and t2 are different to prove that the state is different! "Same state" does not mean "same event", two events on an object's worldline are distinct even if the object was in the same state at both points. Again you are using a weird sort of pseudophilosophical reasoning in your "proof", based on your own vague and nonstandard definitions of terms which have accepted meanings in physics.

As I've said before, it is not permitted to try to dispute mainstream physics on this forum. If there are things you're confused about you can ask about them, but these sorts of confident arguments that accepted ideas are wrong won't fly--please stop it or I will report your posts to the mentors and let them deal with it.
Hurkyl
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Aug25-08, 03:48 PM
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Quote Quote by aranoff View Post
No theory is perfect, which can be proven using Gödel's arguments.
I'm not entirely sure what you mean by 'perfect', but I am virtually certain it's not something that Gödel's theorems talk about.

Quote Quote by aranoff
One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.
(Assuming we limit ourselves to a mathematically simple version of GR in which the metric must be finite and differentiable at all points....)

The 'solution' does exist everywhere inside the black hole. More precisely, the Schwartzchild metric really does exist at each point inside of the black hole, and satisfies the EFE there. The singularity is a hypothetical point whose existence is merely suggested -- not proven -- by the form of the Schwartzchild 'coordinates'. But the criteria imposed above imply that the point really doesn't exist.

(I put 'coordinates' in scare quotes because the Schwartzchild coordinates, taken as a whole, are not actually coordinate functions)
aranoff
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Aug25-08, 04:21 PM
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I forwarded some of your comments to another physics professor. His reply:

You must have seen by now that physicsforums.com is not a good place for any
serious scientist. The noise level of pompous ignorance is too high for a
sensible discussion.

The singularity is proven, not hypothetical.
Hurkyl
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Aug25-08, 04:28 PM
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I'm curious -- if you didn't want to listen to a word that anybody here is saying, then why did you post?
JesseM
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Aug25-08, 05:32 PM
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Quote Quote by aranoff View Post
I forwarded some of your comments to another physics professor. His reply:

You must have seen by now that physicsforums.com is not a good place for any
serious scientist. The noise level of pompous ignorance is too high for a
sensible discussion.
Did he have any specific criticisms of claims or arguments made on this thread?
Quote Quote by aranoff
The singularity is proven, not hypothetical.
What do you (or he) mean by that? If you're saying it's proven that black holes must form singularities according to GR, of course that's true, no one has disputed this, unless Hurkyl was disputing it above in which case I believe he is simply incorrect (my understanding is that the necessity of real physical singularities inside the event horizons of black holes according to GR was proved by the Penrose-Hawking singularity theorems). The point is that most physicists would expect that a theory of quantum gravity would predict something different about the center of the black hole, although they don't expect the predictions of a theory of quantum gravity would significantly diverge from those of GR until we reach the Planck scale.
aranoff
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Aug25-08, 07:32 PM
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Quote Quote by JesseM View Post
The point is that most physicists would expect that a theory of quantum gravity would predict something different about the center of the black hole, although they don't expect the predictions of a theory of quantum gravity would significantly diverge from those of GR until we reach the Planck scale.
I'm sorry, but I am at a loss of how to communicate with you guys. You are supposed to be physicists, either students or professors. I said very clearly that I was discussing the meaning of GR, and you mention quantum gravity!

Why did I post? Well, based upon your emotional reactions and immature thinking, I cannot recommend Physics Forums to my colleagues or students. I am very disappointed.

You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.
JesseM
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Aug25-08, 08:03 PM
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Quote Quote by aranoff View Post
I'm sorry, but I am at a loss of how to communicate with you guys. You are supposed to be physicists, either students or professors. I said very clearly that I was discussing the meaning of GR, and you mention quantum gravity!
As I understand it, you are not discussing purely theoretical questions about what GR predicts (it predicts singularities, and there is nothing a priori impossible about the idea that these could be real physical entities), but rather the empirical question of whether GR's predictions are correct (you reject its predictions everywhere inside the event horizon for reasons that aren't really clear, while most physicists have physical reasons for thinking its predictions are only likely to go significantly wrong at the Planck scale). Am I misunderstanding something here?
Quote Quote by aranoff
Well, based upon your emotional reactions and immature thinking,
Insulting other people's arguments in this way without actually addressing what's wrong with them seems like a knee-jerk emotional reaction to me.
Quote Quote by aranoff
You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.
your profile doesn't say what your full name or educational background is, only that you are a substitute teacher in high school. You can see my full name if you look at the website linked to in my profile (I don't have any particular desire to see this thread be one of the top results on google for my name so I won't mention it). I majored in physics in college as an undergraduate, I don't claim to have any great expertise in GR but I have read enough to know that your arguments contradict the understanding of most professional physicists.
DaleSpam
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Aug25-08, 08:10 PM
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Quote Quote by aranoff View Post
You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.
Names, emails, affiliations, and status are appropriate for a peer-reviewed manuscript, not for an internet forum. I think you misunderstand the nature of an internet forum if you expect such things. This forum is not intended to be a substitute for traditional education nor is it intended to be a substitute for the peer-reviewed literature. Your expectations seem unrealistic.
aranoff
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Aug25-08, 08:54 PM
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My discussions were what does GR predict.

I am a physics professor, and have been for many years. My website gives a paper I wrote on the topic in 1972. I am sort of retired, and so do some high school subbing.
Mentz114
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Aug25-08, 09:16 PM
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Quote Quote by aranoff View Post
My discussions were what does GR predict.
aranof,

You don't seem to understand what GR predicts. I've been following this thread and I've read it more than once. You started by not accepting that the infinite time to reach the event horizon is observer dependent, then changed to your position when this was pointed out. Your argument that the singularity at r=0 invalidates GR has also been refuted.

I take all your subsequent remarks about the forum as sour grapes.

M
JesseM
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Aug25-08, 09:22 PM
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Quote Quote by aranoff View Post
My discussions were what does GR predict.
So all discussions about whether GR's predictions are correct or incorrect are irrelevant, then? Why the long discussion about rejecting the predictions inside the event horizon? GR predicts a singularity at the center, end of story. There is nothing logically impossible about this prediction, so no reason to reject such a solution a priori.
Quote Quote by aranoff
I am a physics professor, and have been for many years.
What area of physics? Do you have much expertise in general relativity? (this would seem unlikely, given that you apparently didn't realize the proper time for a falling observer to cross the event horizon is finite, and given that you seem to use terms like 'solution' and 'boundary condition' and 'state' differently than they are used by physicists in relativity)
Hurkyl
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Aug26-08, 03:46 AM
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Quote Quote by JesseM View Post
unless Hurkyl was disputing it above in which case I believe he is simply incorrect (my understanding is that the necessity of real physical singularities inside the event horizons of black holes according to GR was proved by the Penrose-Hawking singularity theorems).
The thing is that the singularity doesn't occur at a point in space-time. GR doesn't demand that the inside of a black hole have the topology of a ball -- instead, a Schwartzchild black hole has the topology of the 3-dimensional analog to an (open) annulus. The r=0 points are inside the hole, rather than being parts of space-time.

(If we interpret Schwartzchild coordinates as if spacelike slices gave spherical coordinates on 3-space, the hole consists of a single point)


Yes, if we so desired, we can remove this interesting topological feature by filling it with a point and relaxing the condition that the metric be everywhere defined. But I don't believe that to be a good idea, since it gives up your ability to prove things by reasoning topologically. (And, of course, it is a bad idea if you're someone who absolutely insists that the metric be everywhere defined and differentiable)
atyy
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Aug26-08, 05:26 AM
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Not sure whether these should go here, since the thread has deviated towards aranoff's questions. But while staying on the subject of his questions:

Would anyone care to comment on whether the cosmic censorship hypothesis is necessary for GR to make sense?

Do we have any experimental evidence for singularities as predicted by GR?

Weinberg comments in his 1972 text that the singularity theorems only prove that a singularity existed some time in the past, but need not fill all of spacetime. Is this true? Taking "big bang" theory to be the most commonly accepted cosmology, does it mean that a singularity is not an essential part of "big bang" theory?
coelho
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Aug26-08, 05:43 AM
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Well... from a philosophycal point of view, to deny the existence of the inside of the EH for a physicist is the same that to deny the existence of a Heaven for a religion person.

The religious says that there is a Heaven some people goes after dying. We who are alive never see it. We see the dead corpse rotting, nothing else. And nobody ever returned from this so-called Heaven to tell us it actually exists. They say only when we die we will know it.

The physicists says that there is spacetime, and a singularity inside the EH. But we, outside observers, cant observe it, nor it can influence the outside of the EH, so we have not any means to know what is like inside there. If we throw something into a black hole, we only see it going nearer and nearer the EH, but never crossing it. For one were able to see how is inside the EH, one must fall into it.

The likeness is striking. And, while i dont say i disagree with all the physical "knowledge" about GR, i must admit that this knowledge is no more philosophically "solid" than the belief in the existence of Heaven is for the religious people.

Science must make falsifiable predictions. But if we can never know what happens inside the EH, how can we test any predictions concerning there? The argument that the spacetime must follow the same laws of the physics anywhere will be only an (probably methaphysical) assumption if we were not able to test it or its effects. And as we cant know for sure if it is so, we cant assume it is.
DaveC426913
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Quote Quote by coelho View Post
The religious says that there is a Heaven

The physicists says that there is spacetime

The likeness is striking.
Well, except for the fact that we can create mathematically-consistent models from what we do know. The same can't be said in both cases.
JesseM
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Quote Quote by Hurkyl View Post
The thing is that the singularity doesn't occur at a point in space-time. GR doesn't demand that the inside of a black hole have the topology of a ball -- instead, a Schwartzchild black hole has the topology of the 3-dimensional analog to an (open) annulus. The r=0 points are inside the hole, rather than being parts of space-time.

(If we interpret Schwartzchild coordinates as if spacelike slices gave spherical coordinates on 3-space, the hole consists of a single point)


Yes, if we so desired, we can remove this interesting topological feature by filling it with a point and relaxing the condition that the metric be everywhere defined. But I don't believe that to be a good idea, since it gives up your ability to prove things by reasoning topologically. (And, of course, it is a bad idea if you're someone who absolutely insists that the metric be everywhere defined and differentiable)
So when you say singularities don't have to exist in GR, do you just mean that we can remove the exact point of the singularity from spacetime, while leaving the tensors at every other point in spacetime unchanged? If we lived in a universe exactly described by GR, presumably there'd be no empirical difference between these two models, since all measurements would be made at observers who are at some finite separation from the point where the singularity would be, and all the observations associated with it--the way objects get crushed as they approach it and the curvature approaches infinity, and the way worldlines in its neighborhood end after a finite proper time--would still hold true.
Hurkyl
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Aug26-08, 02:37 PM
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Quote Quote by JesseM View Post
So when you say singularities don't have to exist in GR, do you just mean that we can remove the exact point of the singularity from spacetime, while leaving the tensors at every other point in spacetime unchanged?
Right. And as far as I know, that's how things are usually treated. (But that could just be a function of my reading interests) I personally cannot think of any real advantage to adding that point to space-time. (Actually, there's no obvious reason why it should just be a single point that's added in....)


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