Crossing the event horizon of a black hole

[JesseM]

The gravitational field is continuous as one passes through the surface. Consider a uniform mass. As the test particle enters the mass, we draw a sphere, center the planet, radius the distance to the test particle. We calculate the mass of the sphere, and use this mass to calculate the field.

I wasn't talking about the gravitational field (curvature tensor), I was talking about a discontinuity in the values of the stress-energy tensor which defines the distribution of matter and energy in the spacetime, and which is related to the curvature tensor by the Einstein field equations in GR. My point is that although the manifold on which the tensors of GR are defined may be required to be continuous, there is definitely no requirement that the values of the tensors themselves should vary continuously. I challenge you to find a single textbook or paper by a professional physicist which states that a spacetime with a discontinuity in the values of the tensor should be thrown out. Of course you won't, because that would imply physicists throw out the interior regions of black holes as well as cosmologies including a Big Bang singularity (which is not separated from the rest of the universe by an event horizon), while any GR textbook will contain detailed discussions of these solutions.

According to the external observer, there is no spacetime inside the BH.

Irrelevant to your previous argument, you said we should throw out any "solution" which includes a singularity, and at a mathematical level the entire BH spacetime (inside and out) is a single solution to the Einstein field equations, the fact that the region inside the horizon is not observable by anyone who doesn't cross it doesn't make that region a separate "solution". You are just inventing ad hoc ways of justifying your prejudices using poorly-defined terminology, not making any rigorous argument against the validity of GR anywhere inside the horizon.

The same is what happens as we approach a BH, due to the geometry. Remember that the geometry is not Euclidean. We can imagine falling forever towards the BH. No matter where we are, we can continue further. As we fall, time marches on. The distance to the BH is infinite. No matter how long we wait and how close we get to the event horizon, we can always imagine waiting longer and getting closer. There is no end point. This is what I meant by my statement "the event horizon is geometrically the same as a straight line." Sorry for the confusion. The topic is confusing enough!

Nonsense, any textbook on black holes will tell you that for an observer falling into the BH, the proper time (time as measured by a clock falling with them) to cross it is finite. The coordinate time in Schwarzschild coordinates to cross it is infinite, but there is nothing special about Schwarzschild coordinates, one can use other coordinate systems such as Eddington-Finkelstein coordinates where the time to cross it is finite, it is really only proper time that has physical significance (one could even come up with a coordinate system where it takes an infinite coordinate time for you to cross from one end of your room to the other).

You say we need another theory, which you call quantum gravity. This means you agree that GR alone is not valid inside the BH. We agree.

Wrong, I simply echo physicists in saying GR is not valid at the Planck scale. The energy densities would only approach the Planck density very close to where GR predicts a singularity (probably in the neighborhood of one Planck length from it), in regions of the interior far from the singularity there's no such reason for thinking GR would significantly disagree with quantum gravity (except perhaps in the case of the inner horizon of a rotating black hole, which calculations suggest would see infinitely blueshifted light from outside, again creating energy densities greater than the Planck density).

I am not interested in discussing possible future developments in physics. I am focused in understanding current theories as they are. My point is GR (today's GR, not the future GR) is not valid inside the BH.

Indeed, this forum is not a place to debate interpretations of GR which are widely accepted among physicists, as you are doing by rejecting everything inside the horizon--you will find no textbooks which agree with you, or that say that solutions with discontinuities in tensor fields should automatically be rejected, this is just stuff you're making up with no justification. Please read the IMPORTANT! Read before posting thread at the top of the forum, attempting to disprove mainstream views on GR is explicitly forbidden, if you continue to do so I'll report your posts.

 

[aranoff]

Okay, let me understand you. We agree that T can be discontinuous. We agree that if we reject the singularity, then G is discontinuous. You therefore say that it is acceptable in GR for G to be discontinuous? What are the implications of this? Any other examples of G being discontinuous?

" challenge you to find a single textbook or paper by a professional physicist which states that a spacetime with a discontinuity in the values of the tensor should be thrown out."
Again, you agree that the solution of GR at the center of the BH is not valid. We agree! Since it is not valid there, it is not valid anywhere. If you do not like my continuity argument, okay. I actually view it as a boundary condition saying this solution is not valid. Why do you reject my boundary condition reasoning?

"a Big Bang singularity (which is not separated from the rest of the universe by an event horizon), while any GR textbook will contain detailed discussions of these solutions."
It is fine to have discussions. It is not fine to say that cosmology including the Big Bang singularity is a valid physical theory, as it contains a mathematical inconsistency. Instead, it is a working hypothesis, which hopefully will become part of a future theory. BTW, have you heard of Rosen's cosmology, in which there is no infinite big bang?

We must focus on the basic principles of physics. We cannot say just because this is what physicists say it must be so. Physicists said von Laue current is valid. I had to fight this to get my paper published in 1972. If you were the group moderator then, you would not have permitted my paper to appear on the site. I was amazed at the wrong ideas most physicists had, 75 years after SR, which is a simple theory.

What I insist is clear statements of basic principles and the conclusions drawn from them.

Why are you talking about Planck, when we are discussing GR, not QM?

What about the principle that if something cannot be observed in principle, it does not exist? The "finite time to cross the event horizon", as predicted by GR, cannot be observed in principle!

 

[MeJennifer]

According to the external observer, there is no spacetime inside the BH.

That statement is wrong as the existence of any region of spacetime is observer independent.

The event horizon simply signifies that no signals from events inside can be observed from the outside of the event horizon. The event horizon functions like a one-way membrane.

 

[aranoff]

When I said spacetime does not exist inside the BH, I am relying on the fundamental principle of physics which states that something that cannot be observed in principle does not exist. This principle is more basic than GR or QM or whatever.

 

[DaveC426913]

the fundamental principle of physics which states that something that cannot be observed in principle does not exist.

Well... it can be observed in principle (and by a non-hypothetical observer, too), it's just that those observations cannot be communicated back.

 

[Hurkyl]

When I said spacetime does not exist inside the BH, I am relying on the fundamental principle of physics which states that something that cannot be observed in principle does not exist. This principle is more basic than GR or QM or whatever.

You cannot strictly adhere to that principle without running into all sorts of problems. For example, it leads directly to strict solipsism which rejects the existence of anything but your own mind.

GR has its own pecular reason why it's a bad idea to allow regions of space-time to be excised from existence: sure, the mathematics is consistent with the inside and EH of a black hole being non-existant. But it is also consistent with there being a 1-foot-in-diameter ball of non-existant space-time that moves around so that it's 2 feet directly in front of your face.

This principle has never excluded indirect observation; we detect the effects of what GR calls a black hole, and so we infer the existence of what GR calls a black hole.

Finally, research into quantum gravity has suggested that the insides are (eventually) directly observable anyways.

We can imagine falling forever towards the BH.

We can, but it wouldn't be relevant. If I pilot my spaceship into a black hole, then GR predicts I will get there within a finite amount of time, as measured by my wristwatch. The interesting thing is that, if I can avoid being crushed, I will also run off of the edge of space-time within a finite amount of time.

 

[aranoff]

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]

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".

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!

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).

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?

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]

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.

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]

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]

I'm curious -- if you didn't want to listen to a word that anybody here is saying, then why did you post?

 

[JesseM]

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?

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]

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]

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?

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.

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.

 

[Dale]

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]

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]

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]

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.

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]

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]

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]

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, can't 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 don't 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 can't know for sure if it is so, we can't assume it is.

 

[DaveC426913]

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]

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]

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...)

 

[aranoff]

Okay, you claim that you won the argument, and I have sour grapes. Let's clarify exactly what you say.

We are discussing GR only, not QM.

The solution of GR from the point of view of the falling observer is valid everywhere except at the mathematical point of the center of the BH. At this point, there is a singularity, which means that the solution is not valid here.

Although it is not possible to observe the falling of the observer through the event horizon, as it takes forever, this solution is still meaningful, for the observer himself is capable of observing the event. The analogy with the meaninglessness of Heaven, a concept that no observer except a dead person, can observe, is not relevant. The fact that the observer loses all thoughts once he crosses the horizon, because the only things meaningful about a BH are mass, angular momentum, and charge, does not detract from the validity and meaningfulness of the solution. The fact that nothing changed as the object fell from one point inside to another point inside still permits us to describe coordinates of the falling observer inside the BH.

Is this your position?

I still did not get how you can justify this.

 

[JesseM]

Okay, you claim that you won the argument, and I have sour grapes. Let's clarify exactly what you say.

Who are you addressing here? Mentz114, who made the "sour grapes" comment? Me? Hurkyl? Someone else?

We are discussing GR only, not QM.

If we are purely discussing what is predicted theoretically by GR, then all discussions of whether GR is empirically valid are off-limits, no?

The solution of GR from the point of view of the falling observer is valid everywhere except at the mathematical point of the center of the BH. At this point, there is a singularity, which means that the solution is not valid here.

What do you mean by the word "valid" mean here, if it has nothing to do with empirical validity?

Although it is not possible to observe the falling of the observer through the event horizon, as it takes forever, this solution is still meaningful, for the observer himself is capable of observing the event. The analogy with the meaninglessness of Heaven, a concept that no observer except a dead person, can observe, is not relevant. The fact that the observer loses all thoughts once he crosses the horizon, because the only things meaningful about a BH are mass, angular momentum, and charge, does not detract from the validity and meaningfulness of the solution.

Here you once again jump to conclusions about a subject you have obviously not studied beyond a superficial level. The only observable attributes of a BH as viewed from the outside the event horizon are mass, angular momentum, and charge (according to GR), but this does not mean there can't be all sorts of interesting stuff going on inside the horizon, like observers making measurements and having thoughts as they fall towards the singularity.

 

[Hurkyl]

The solution of GR from the point of view of the falling observer is valid everywhere except at the mathematical point of the center of the BH. At this point, there is a singularity, which means that the solution is not valid here.

Why do you continue to insist that there a point at the 'mathematical center' of a BH? GR does not demand that the interior of a black hole have the topology of a ball -- in fact, it demands exactly the opposite if you use a formulation that rejects singularities. Colloquially speaking, there must be at least one point 'missing'. (Or something else much more exotic, like a wormhole)

You seem to have no problem with a space-time manifold for which the entire black hole is 'missing'. Why do you have a problem with a space-time manifold for which a single point is 'missing'?


As an aside, if you are allowing 'generalized' fields (e.g. distributional fields) that have singularities and other bad behavior... then you really ought to be using the corresponding 'generalized' notion of a partial differential equation (e.g. distributional derivatives). In that case, a field can still satisfy the EFE, even if it has singularities.

The fact that the observer loses all thoughts once he crosses the horizon, because the only things meaningful about a BH are mass, angular momentum, and charge, does not detract from the validity and meaningfulness of the solution. The fact that nothing changed as the object fell from one point inside to another point inside still permits us to describe coordinates of the falling observer inside the BH.

You have misunderstood the no hair theorem -- while such information is inaccessible to observers outside the event horizon, it is by no means inaccessible to observers inside the event horizon. In fact, in order to even make the quoted statement, you had to assume that there were physically distinct states inside the black hole!


There is another thing; physical theories routinely allow us to infer the existence of things we cannot directly observe. This is, in fact, necessary. There is merit to waxing philosophically about which things we should infer exist and which things we shouldn't -- but IMHO you're being far too absolute about things.


Incidentally, I feel compelled to state that the notion of a point is not physically meaningful in GR (really, it isn't meaningful even in Newtonian mechanics!). I assume you already know this and are referring to something that is meaningful (e.g. the point where the infalling observer's wristwatch read 3:00 PM), but I want to make absolutely sure that there wasn't a conceptual problem being obscured by this abuse of language.

 

[coelho]

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.

Yes... but mathematical consistence does not mean anything by itself. The mere fact one theory is mathematically consistent does not imply its a valid theory to describe a physical phenomena, if it were not testable in the "real world".
Testing hypotheses derived from the theorethical framework against the experiences is a necessary step of the scientific method, and if this one can't be done in some class of phenomena, then this phenomena can't be completely "scientifically" treated, and some degree of "faith" is required to admit the validity of any theory used to describe this phenomena, as we don't have the proof of the experimental facts to ensure its validity.

 

[aranoff]

You have misunderstood the no hair theorem -- while such information is inaccessible to observers outside the event horizon, it is by no means inaccessible to observers inside the event horizon. In fact, in order to even make the quoted statement, you had to assume that there were physically distinct states inside the black hole!

What do you mean by an observer inside the BH? The only property the observer has is mass. Furthermore, as the observer falls, the angular momentum of the BH does not change. When we speak about observers inside a BH is like talking about observers who observe Heaven after death. As the dead observers move to different parts of Heaven, nothing changes for the external observers (the living).

I am sick and tired of mixing religion and science. With science, look at the theory. The math must be consistent. The results must be capable of verification or falisfaction.

Indeed, I am suspicious that one reason for the popularity of the Big Bang is the idea that maybe God created the universe.

Your insistence on talking about the inside of the BH may be due to some type of religious thinking.

The BH is not an excluded point. It is simply an end to the universe. The spherical universe has no end. Travel out at a constant speed in a straight line for a time t. Wait longer, and you are still in the universe. Same if we approach a BH. Just that the geometry is not Euclidean, and this confuses you.

 

[aranoff]

There is another thing; physical theories routinely allow us to infer the existence of things we cannot directly observe. This is, in fact, necessary. There is merit to waxing philosophically about which things we should infer exist and which things we shouldn't -- but IMHO you're being far too absolute about things.

We can infer things that we cannot observe, but must be capable of observing in principle.

E.g., superfluid helium. We cannot observe the positions of the atoms, except to say that they are in the container. Therefore, the positions do not exist, because we cannot observe it in principle.