B Confusion regarding black hole spin

[PeterDonis]

it's not clear whether he's referring to the maximal analytic extension or not, but in any case he didn't ask about real black holes in the universe

If he's not referring to the maximal analytic extension (which I doubt he is), then he is talking about some other model which only has a portion of the spacetime being Kerr, with the rest being a region of collapsing matter--i.e., a spacetime model of a real rotating black hole that formed by gravitational collapse. The fact that the OP didn't explicitly say that does not mean it's not the appropriate kind of model to be thinking of in this discussion.

What I've said is that even if we can model the collapse with GR, that doesn't mean GR is valid inside the black hole.

On what grounds are you making this extraordinary claim? If you mean that you don't think GR can model collapsing matter once it's inside the event horizon, that is also wrong.

The theory that could describe the matter inside doesn't yet exist

Nonsense. GR doesn't magically stop working at an event horizon. It can model matter inside an event horizon just fine.

 

[PeterDonis]

Is ADS in GR a vacuum solution or not?

It depends on what you consider a "vacuum" solution. If you consider the cosmological constant to be a form of stress-energy, then no. If you don't, then yes. Both viewpoints are consistent with the math.

 

[DaveC426913]

Counting from the outside, the second white line is what you might call the actual edge of the black hole if you could see it without the gravitational effects. The black region is the size you would actually see.

So the diameter of the EH is significantly smaller than the apparent disc of the BH to an observer, thus?

 

[javisot]

On what grounds are you making this extraordinary claim? If you mean that you don't think GR can model collapsing matter once it's inside the event horizon, that is also wrong.

Nonsense. GR doesn't magically stop working at an event horizon. It can model matter inside an event horizon just fine.

Just to clarify, Peter, if one day I write a thread titled "GR is valid inside a black hole" (remember that inside a black hole described by GR there is a singularity where GR ceases to be valid), and "in GR, ADS it's not a vacuum solution", do you confirm that I will not be banned?

 

[Ibix]

So the diameter of the EH is significantly smaller than the apparent disc of the BH to an observer, thus?

Yes. I think you've taken the animation still at a lot higher $a$ than Gargantua is modelled so that's a good deal more asymmetric.

 

[Ibix]

Just to clarify, Peter, if one day I write a thread titled "GR is valid inside a black hole" (remember that inside a black hole described by GR there is a singularity where GR ceases to be valid)

I think everyone agrees that GR goes wrong somewhere, and it's probably not significantly wrong until inside the horizon for macroscopic (stellar mass and above) black holes. So I think GR can reasonably be used to describe matter in some regions inside a hole, but not all. I suspect you and @PeterDonis are reading what you wrote in different ways, as either an absolute statement about the entire interior versus "it must go wrong somewhere".

"in GR, ADS it's not a vacuum solution"

I think that depends what you mean by a vacuum solution. If you believe $\Lambda$ is an energy of the vacuum, yes it is. If you believe $\Lambda$ is some uniform dark energy, no it's not.

 

[javisot]

I think everyone agrees that GR goes wrong somewhere, and it's probably not significantly wrong until inside the horizon for macroscopic (stellar mass and above) black holes. So I think GR can reasonably be used to describe matter in some regions inside a hole, but not all. I suspect you and @PeterDonis are reading what you wrote in different ways, as either an absolute statement about the entire interior versus "it must go wrong somewhere".

Agree.

I think that depends what you mean by a vacuum solution. If you believe $\Lambda$ is an energy of the vacuum, yes it is. If you believe $\Lambda$ is some uniform dark energy, no it's not.

I can't agree with this. A vacuum solution is defined by having a stress-energy tensor equal to zero. Saying "ADS in GR is not a vacuum solution" is equivalent to saying that in that solution the stress-energy tensor is not equal to 0.

 

[PeterDonis]

Just to clarify, Peter, if one day I write a thread titled "GR is valid inside a black hole" (remember that inside a black hole described by GR there is a singularity where GR ceases to be valid), and "in GR, ADS it's not a vacuum solution", do you confirm that I will not be banned?

No, I will not confirm any such thing. Moderators here can't make any statements about posts that have not been made.

I suggest that you stop trying to make dogmatic statements about terminology and start thinking about what GR actually says. Whether or not you call a particular solution a "vacuum solution" is a matter of words, not physics; the solution is what it is and makes whatever predictions it makes regardless of whether we use the term "vacuum solution" to describe it.

As for where GR is "valid", that's also a word that ignores all the actual issues involved. What is true is that if we live in a spacetime that has an actual event horizon, and we remain outside the event horizon, we can never get direct evidence of events inside the horizon. But that in no way means that we can't get indirect evidence about such things, and compare that with what our models predict.

 

[PeterDonis]

A vacuum solution is defined by having a stress-energy tensor equal to zero.

And then you get to choose whether the "stress-energy tensor" includes the cosmological constant term or not. As I've already said, both viewpoints, that it is and that it isn't, are consistent with the math.

Saying "ADS in GR is not a vacuum solution" is equivalent to saying that in that solution the stress-energy tensor is not equal to 0.

Yes, it is. So what? There is a viewpoint in which that is indeed the case.

Again, you need to stop making dogmatic statements about terminology and start focusing on the actual physics, which doesn't care whether or not we call AdS a "vacuum solution" or whether we call the cosmological constant term part of the stress-energy tensor. The models make the same predictions either way.

 

[javisot]

And then you get to choose whether the "stress-energy tensor" includes the cosmological constant term or not. As I've already said, both viewpoints, that it is and that it isn't, are consistent with the math.


Yes, it is. So what? There is a viewpoint in which that is indeed the case.

Again, you need to stop making dogmatic statements about terminology and start focusing on the actual physics, which doesn't care whether or not we call AdS a "vacuum solution" or whether we call the cosmological constant term part of the stress-energy tensor. The models make the same predictions either way.

https://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)

"In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums can be taken as cosmological models).

More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes.

Vacuum solutions are a special case of the more general exact solutions in general relativity."

"In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This can be interpreted physically as a kind of classical approximation to a nonzero vacuum energy."

 

[PeterDonis]

https://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)

Wikipedia is not a valid reference for something like this. The Wikipedia article does give Stephani's monograph as a source, but does not give any specific quotes from it.

That said, note that in that article, the Einstein Field Equation is given without the cosmological constant term, and in its listing of vacuum solutions, AdS does not appear.

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.

And by this definition, AdS is not a vacuum solution, since its Einstein tensor does not vanish; it's equal to $\Lambda g_{ab}$, where $\Lambda$ is the cosmological constant.

According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically

This is only true if there is no cosmological constant term. See above.

Indeed, the article itself points this out:

"In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This can be interpreted physically as a kind of classical approximation to a nonzero vacuum energy."

So by this definition, AdS is a lambdavacuum solution, which is not the same as a vacuum solution. Note that the article here is adopting the viewpoint I referred to in earlier posts, which treats the cosmological constant term as part of the stress-energy tensor.

@javisot, you are hijacking someone else's thread, and you don't have a sufficient understanding of the topic you're trying to post about. Therefore, I have now banned you from further posting in this thread.