B Confusion regarding black hole spin

[Dark85]

TL;DR Summary

If we consider a black hole that spins(A Kerr black hole), what exactly is spinning?

Hey guys I have a question,
When we say a black hole spins, what exactly is spinning? Isn't a black hole just a region of spacetime from which light cannot escape? If so, then can space time rotate, which is why we say black holes rotate?

 

[javisot]

https://en.wikipedia.org/wiki/Frame-dragging

 

[Dark85]

https://en.wikipedia.org/wiki/Frame-dragging

Hey thanks a lot, but can you please explain. I am still in 10th grade, i don't quite understand frame-dragging.

 

[javisot]

Hey thanks a lot, but can you please explain. I am still in 10th grade, i don't quite understand frame-dragging.

This is one of those things that to understand you should go to the last section "Mathematical Derivation" and understand what is stated there. (maybe some veteran can translate it into accessible language)

 

[Dark85]

This is one of those things that to understand, you should go to the last section "Mathematical Derivation" and understand what is stated there

 

[PeroK]

TL;DR Summary: If we consider a black hole that spins(A Kerr black hole), what exactly is spinning?

Hey guys I have a question,
When we say a black hole spins, what exactly is spinning? Isn't a black hole just a region of spacetime from which light cannot escape? If so, then can space time rotate, which is why we say black holes rotate?

The simplest answer is that the giant star that created the black hole had angular momentum. That angular momentum is inherited by the black hole. This affects the spacetime around the star and black hole.

 

[Dark85]

The simplest answer is that the giant star that created the black hole had angular momentum. That angular momentum is inherited by the black hole. This affects the spacetime around the star and black hole.

Yeah I did think about that, but if a black hole is a region in space time, does it really make sense for "space time" to have angular momentum? I'm still confused.

 

[PeroK]

Yeah I did think about that, but if a black hole is a region in space time, does it really make sense for "space time" to have angular momentum?

It makes sense to me! Angular momentum is one of the fundamental quantities in nature.

 

[Dark85]

It makes sense to me! Angular momentum is one of the fundamental quantities in nature.

Yeah I know that but can a thing like space time possess angular momentum is my question.

 

[javisot]

Yeah I know that but can a thing like space time possess angular momentum is my question.

It can even have entropy, in certain theories, but that's another topic. Consider that angular momentum comes from the process that ends in a black hole, not from the black hole itself.

 

[Dark85]

It can even have entropy, in certain theories, but that's another topic. Consider that angular momentum comes from the process that ends in a black hole, not from the black hole it

I am beginning to get a little understanding, will think about it, thank you for your help!

 

[Ibix]

Yeah I know that but can a thing like space time possess angular momentum is my question.

The maths says yes. And the same maths lets us make accurate predictions of other things. So yes, it apparently does make sense, counterintuitive though it may seem.

It's worth remembering that our intuition about physics is built up in a fairly middle-of-the-road low energy, low speed environment. Reality includes a lot of circumstances that aren't like that and our every-day intuition fails us. You have to build and test mathematical models for those circumstances, and then you can build up intuition about those.

It's also worth noting that we have a lot of reasons to suspect that general relativity goes wrong somewhere inside a black hole. So it's possible that "spacetime can have angular momentum all on its own" is a feature of general relativity and not of whatever future theory we come up with. Nevertheless, it is a feature of a pretty solid mathematical model, so we accept it as a pretty solid fact.

 

[PeterDonis]

can a thing like space time possess angular momentum

To understand how that can be the case, you have to understand that in General Relativity, "angular momentum" of any system--even an ordinary spinning planet or star--can be understood as a property of the spacetime geometry around the system. (This is also true of mass, by the way--that's why a black hole, even a non-spinning one, can have mass even though it's entirely vacuum, there's no matter anywhere.)

The mathematical details of how this is done are probably too advanced for your current level of knowledge, since you say you're only in 10th grade and you probably have not learned much physics. But the basic idea is that you look at how objects move in the spacetime around the system, and you use those motions to measure the mass and angular momentum of the system. For example, you can measure the mass of the Sun by measuring the orbital parameters of the planets orbiting the Sun--their mean distances and their orbital periods--and then using Kepler's Third Law.

Measuring angular momentum this way is more complicated; you have to put gyroscopes in orbit around the spinning object and measure how they precess. This is a measurement of the "frame dragging" that was mentioned in other posts. The Gravity Probe B experiment did this for the Earth:

https://en.wikipedia.org/wiki/Gravity_Probe_B

 

[PeterDonis]

The singularity is not a point mass, it's a space-like line that lies in the future of all worldlines entering the hole.

And that line, the locus $r = 0$, is not even part of the spacetime manifold at all, as far as the actual math is concerned.

 

[DaveC426913]

Followup question to OP, though i think PD addressed it in post 13: how can one observe this spin? PD mentions gyroscope very close to it but are there other observables?

I assume we can't trust the angular momentum of its accretion disc, since could have come from the infallible matter.

 

[Ibix]

Followup question to OP, though i think PD addressed it in post 13: how can one observe this spin? PD mentions gyroscope very close to it but are there other observables?

I assume we can't trust the angular momentum of its accretion disc, since could have come from the infallible matter.

In principle you can study freefall paths near an object. Gravitational lensing near a spinning black hole produces different results depending on the angular momentum because the light is dragged in a spinwards direction. If you look at pictures of the black hole in Interstellar (modelling by Nobel prize winner Prof Kip Thorne), what is actually there is a black oblate spheroid with a fairly narrow glowing ring (the accretion disc) around it. The multiple copies of the ring and the halo around the hole come from light orbiting the hole multiple times before coming to us, and the asymmetry comes from light being dragged spinwards by the gravity of the spinning hole. The higher the angular momentum the more the dragging.

We don't have high enough resolution images of an actual black hole to confirm that this model is accurate. But we expect it to be.

The gyroscope method Peter mentions is much more sensitive. We've actually done it near Earth and detected evidence of frame dragging.

 

[javisot]

¿The rotation of the black hole and therefore the frame dragging can affect the ringdown after the merger of two black holes detected in LIGO-Virgo? (I would say yes but I'm not sure)

 

[DaveC426913]

I assume we can't trust the angular momentum of its accretion disc, since could have come from the infallible matter.

*infalling.

Thanks, @renormalize, for catching that. :)

 

[DaveC426913]

... a black oblate spheroid with a fairly narrow glowing ring (the accretion disc) around it. The multiple copies of the ring and the halo around the hole come from light orbiting the hole multiple times before coming to us, and the asymmetry comes from light being dragged spinwards by the gravity of the spinning hole.

Ah! So it's literally visible.

I thought multiple rings were simply a matter of light rays taking marginally different paths tangent to the photon sphere, closer ones orbiting more times than farther ones before escaping again. I didn't think it had anything to do with frame dragging. TIL.

Does that mean a non-rotating BH won't have these rings?

 

[PeterDonis]

Does that mean a non-rotating BH won't have these rings?

No, but it does mean the rings around a non-rotating BH won't show the asymmetry that was described, which is due to frame dragging.

 

[WWGD]

No, but it does mean the rings around a non-rotating BH won't show the asymmetry that was described, which is due to frame dragging.

What are the center, axes of rotation of the BH?

 

[PeterDonis]

What are the center, axes of rotation of the BH?

The BH has no center, and its axis of rotation doesn't work like you're thinking. A rotating BH is not like an ordinary spinning object.

The correct technical definition of the axis of rotation of a stationary, axisymmetric spacetime (which includes a rotating BH) is "A" level material and this is a "B" level thread, but it can be found in Wald, section 7.1, for those who are interested.

 

[Ibix]

I thought multiple rings were simply a matter of light rays taking marginally different paths tangent to the photon sphere, closer ones orbiting more times than farther ones before escaping again.

That's correct, as Peter has already noted. But look closely at the image at the top of this page: https://www.planetary.org/space-images/interstellar-black-hole. The innermost ring of the "halo" is not concentric with the rest, and the whole halo is noticeably off center from the disc. Those two features are optical effects of the angular momentum.

Wikipedia has a really nice animation of a black hole with an orange background as you vary the spin parameter from 0 (non-rotating) to 1 (maximum possible angular momentum). 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. (I note that the image is generated by yukterez, who I assume is @Yukterez, occasional poster here.)

IIRC, Gargantua was modelled with $a\approx 0.3$ on that scale.

 

[Ken G]

It might also help the beginner trying to understand the spirit of general relativity to remember Wheeler's famous way of describing that spirit: "Matter tells spacetime how to curve, and spacetime tells matter how to move." The point is, there is a connection between matter and spacetime that means you cannot think of the spacetime as some kind of inert background through which matter moves, because gravity involves the way the matter interacts with the spacetime. It's like a dance between two partners, so that means concepts like "energy" and "angular momentum" are not properties of one of the dancers alone, it is more like a property of the dance they are doing. When one dancer throws another in the air and they strike a spinning pose aloft, which dancer is responsible for that remarkable effect? That graceful flourish is clearly something they have accomplished together, just like the way angular momentum is a kind of dynamical flourish that comes from all parties involved, including the spacetime. When a black hole forms, it is as if one of the dancers has gone offstage, but the effect they had on their partner still remains.

 

[Ibix]

The point is, there is a connection between matter and spacetime that means you cannot think of the spacetime as some kind of inert background through which matter moves, because gravity involves the way the matter interacts with the spacetime.

While this is true in general, the OP specified a Kerr black hole, which is everywhere vacuum. So, at least in this case, nothing can be a property of anything except spacetime.

 

[PeterDonis]

the OP specified a Kerr black hole, which is everywhere vacuum.

The maximal analytic extension of Kerr spacetime is everywhere vacuum, yes.

But any real black hole in the real universe will not be everywhere vacuum; it will have to have been formed by the gravitational collapse of something that contained actual matter (i.e., nonzero stress-energy), so the spacetime that describes it will have a non-vacuum region.

It's true that one still has to be able to understand black hole properties like mass and angular momentum as properties of the spacetime geometry, since an outside observer to the future of the collapse process has no effective way of observing the actual matter that collapsed to form the hole and seeing what mass and angular momentum it had. But those properties of the spacetime geometry can still be traced back, ultimately, to the properties of the matter that collapsed (and of other matter that fell in afterwards, if there was any significant amount of that). For any real black hole, you can't just stop at the properties of the vacuum spacetime geometry if you want a full understanding of where they come from.

 

[javisot]

The maximal analytic extension of Kerr spacetime is everywhere vacuum, yes.

But any real black hole in the real universe will not be everywhere vacuum; it will have to have been formed by the gravitational collapse of something that contained actual matter (i.e., nonzero stress-energy), so the spacetime that describes it will have a non-vacuum region.

It's true that one still has to be able to understand black hole properties like mass and angular momentum as properties of the spacetime geometry, since an outside observer to the future of the collapse process has no effective way of observing the actual matter that collapsed to form the hole and seeing what mass and angular momentum it had. But those properties of the spacetime geometry can still be traced back, ultimately, to the properties of the matter that collapsed (and of other matter that fell in afterwards, if there was any significant amount of that). For any real black hole, you can't just stop at the properties of the vacuum spacetime geometry if you want a full understanding of where they come from.

Completely agree with Peter, but what Ibix points out is important, the OP specified a Kerr black hole. Dark85 doesn't ask about the real black holes in the universe. It's reasonable to assume that another theory could say something about collapsing matter, but is speculation. No one has seen that theory nor can we share references since it doesn't exist, yet.

A less intuitive case, it is true that in GR black hole with collapse process we can say "the dynamics of spacetime comes from the dynamics of some matter", but in ADS, the stress-energy tensor is still zero, there is no matter nor has there ever been any, and yet it is a spacetime with scalar (negative) curvature.

 

[PeterDonis]

the OP specified a Kerr black hole

Sure, but what does "a Kerr black hole" mean? Are you saying the OP definitely meant by that term "the maximal analytic extension of Kerr spacetime"? I doubt it. A real black hole spacetime, with collapsing matter that has nonzero angular momentum and then a Kerr vacuum region, could just as well be described by the term "Kerr black hole"--but it is not vacuum everywhere, only the Kerr region of the spacetime is.

Dark85 doesn't ask about the real black holes in the universe.

How do you know that? See above.

It's reasonable to assume that another theory could say something about collapsing matter, but is speculation.

Um, what? Are you saying standard General Relativity can't model collapsing matter? It most certainly can.

in ADS, the stress-energy tensor is still zero

Not necessarily. You can treat the negative cosmological constant as a form of stress-energy. In fact treating a cosmological constant that way is more in line with the common modern view that ultimately the cosmological constant comes from some kind of underlying quantum degrees of freedom.

 

[javisot]

How do you know that? See above.

You may have noticed that he didn't ask about "real black holes in the universe", he strictly asked about the Kerr black hole (as you point out, 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).

Um, what? Are you saying standard General Relativity can't model collapsing matter? It most certainly can.

No. 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. The theory that could describe the matter inside doesn't yet exist; this shouldn't be a subject of discussion, I suppose.

 

[javisot]

Not necessarily. You can treat the negative cosmological constant as a form of stress-energy. In fact treating a cosmological constant that way is more in line with the common modern view that ultimately the cosmological constant comes from some kind of underlying quantum degrees of freedom.

Is ADS in GR a vacuum solution or not?

 

[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.