Kerr (rotating) black holes have TWO horizons?

[jmercer]

Okay... this briefly came up in the "Question about nothing" thread, but I promised to ask it in a separate thread so I didn't derail the original discussion.

How is it possible for a rotating black hole to have two horizons???

 

[sol invictus]

How is it possible for a rotating black hole to have two horizons???

The easiest way to understand the causal structure of black holes is to use conformal diagrams. These show a 2-dimensional slice of the spacetime (e.g. the radial and time directions), and they have the characteristic that light rays directed in the radial direction (meaning precisely towards or away from the center of the black hole) move on straight lines at 45 degrees, and (most importantly) that any other excitation moves along a curve that is everywhere more vertical than 45 degrees.

Here's the diagram for a Kerr hole:

It's a little hard to read, but the upper right and lower right boundaries of region I are asymptotic infinity (in the future and past respectively), far outside the hole. The line separating regions I and II is the outer horizon, and the line between II and VI is (part of) the inner horizon.

Those lines are horizons because of the nice characteristic of these diagrams I described above - all physical excitations propagate upwards more steeply than 45 degrees, and therefore anything emitted above one of those lines never makes it to any region further out of the hole.

It should be noted that most physicist believe (with good evidence) that the inner horizon is unstable, in such a way that the smallest perturbation will turn that ^ on the top of region II into a space-like singularity, making the diagram essentially identical to the one on the upper left here:

(NOTE to DrBaltar - the diagram in the lower left is a BH that forms by collapse of infalling spherically symmetric matter. Note that it's almost identical to the diagram I posted in the other thread, except that the infalling matter follows a curved track, and also note that, as before, there is no matter outside the horizon a diamond-shaped region on the upper left of the diagram.)

 

[jmercer]

So if the inner one is perturbed (no idea what it would take to perturb an event horizon!), the interior horizon simply collapses into a singularity - is that correct?

If so... doesn't that imply that there was no singularity originally? Or is that the point - that the rotation was so rapid that the singularity never formed, and became a second horizon??

 

[sol invictus]

So if the inner one is perturbed (no idea what it would take to perturb an event horizon!), the interior horizon simply collapses into a singularity - is that correct?

That's the idea, yes. You perturb it just by throwing something - anything - into it. More realistically, while the thing is forming it will be significantly perturbed, and the solution plotted there will never come into existence.

If so... doesn't that imply that there was no singularity originally? Or is that the point - that the rotation was so rapid that the singularity never formed, and became a second horizon??

Hang on - even in the unperturbed symmetric solution with two horizons, there's still a singularity. It's labeled on that plot as "rho=0 ring physical singularity". (It says that because the Kerr singularity is a ring, unlike the non-rotating BH, where it's more like the entire volume.)

The claim though is that this solution is unrealistically symmetric, and a physical hole that forms by collapse of some not precisely azimuthally symmetric matter will have a causal structure more like that of a non-rotating BH, specifically with a space-like singularity replacing the inner horizon.

 

[jmercer]

That's the idea, yes. You perturb it just by throwing something - anything - into it. More realistically, while the thing is forming it will be significantly perturbed, and the solution plotted there will never come into existence.

Hmm... ok... thanks. I'm having a hard time envisioning how this could actually happen, given the way black holes form and all the matter surrounding them immediately after forming. I don't see how it could ever be unperturbed.

Hang on - even in the unperturbed symmetric solution with two horizons, there's still a singularity. It's labeled on that plot as "rho=0 ring physical singularity". (It says that because the Kerr singularity is a ring, unlike the non-rotating BH, where it's more like the entire volume.)

A... ring? Now, that's very strange indeed. I see that the poles are the only place where the horizons meet. I would assume that the poles align with the center of the ring.

I wonder what the tidal stresses at the poles are like?

The claim though is that this solution is unrealistically symmetric, and a physical hole that forms by collapse of some not precisely azimuthally symmetric matter will have a causal structure more like that of a non-rotating BH, specifically with a space-like singularity replacing the inner horizon.

And I have NO idea what the hell that would be, or how it would differ from a NRBH.

 

[jmercer]

Oh, wait! A RING? you're saying that the singularity is stretched into a ring and has a donut-like horizon around it???

 

[sol invictus]

Hmm... ok... thanks. I'm having a hard time envisioning how this could actually happen, given the way black holes form and all the matter surrounding them immediately after forming. I don't see how it could ever be unperturbed.

You're absolutely right. It's just that it's much, much easier to solve Einstein's equations when there is some symmetry. So the symmetric Kerr solution is known, but of course it's not very realistic. Often perturbing a little and breaking the symmetry doesn't change the solution much qualitatively, but this case appears to be an exception (at least with regard to the interior).

A... ring? Now, that's very strange indeed. I see that the poles are the only place where the horizons meet. I would assume that the poles align with the center of the ring.

The diagram is somewhat misleading for that, because it only shows radius and time. And there are actually two ring singularities, not just one (I think). But again, this stuff (while cool) is probably all totally meaningless for real rotating holes.

I wonder what the tidal stresses at the poles are like?

If you mean the poles of the outer horizon, not very large (if the hole is big). If you mean near the singularities, very large.

And I have NO idea what the hell that would be, or how it would differ from a NRBH.

It differs significantly in various ways, just not in its overall causal structure. For example it has an ergosphere, etc. - basically outside the outer horizon it will look almost exactly the same as the symmetric solution.

 

[sol invictus]

Oh, wait! A RING? you're saying that the singularity is stretched into a ring and has a donut-like horizon around it???

The singularity is a ring, but the horizon is not a torus (donut as you put it) - it's a somewhat squashed sphere. Actually one can prove that all black holes in four dimensions have horizons with spherical topology.

Interestingly the theorem fails in d=5 - there are so-called "black rings", which are rotating black holes with toroidal horizons, and even a "black Saturn" - a round hole surrounded by a black ring.

 

[jmercer]

Cool stuff, and I thank you for the education.

 

[CapelDodger]

That's the idea, yes. You perturb it just by throwing something - anything - into it. More realistically, while the thing is forming it will be significantly perturbed, and the solution plotted there will never come into existence.

Unless it's designed to - however fleetingly.

Now there's an experimental challenge for the far future .

 

[geni]

I'm sure this came up in Stephen Baxter's Xeelee Sequence as a way of escapeing from a ship chaseing you at near light speeds.

 

[DrBaltar]

I think our other thread on black hole formation, which focuses exclusively on classic schwarzschild black holes is probably just purely academic. I think it's a near certainty that a black hole would be rotating.

 

[Cuddles]

I think our other thread on black hole formation, which focuses exclusively on classic schwarzschild black holes is probably just purely academic. I think it's a near certainty that a black hole would be rotating.

Pretty much. Black holes are a little weird, but conservation of angular momentum still holds. It's fairly unlikely that anything could ever form with precisely zero angular momentum.

 

[INRM]

So there are black holes, black rings, and black holes with black rings?

Have black-rings ever appeared in nature? Have black holes with black rings appeared in nature?

How fast would the rotation of a black-ring be to keep it as a ring and not a black-hole?


INRM

 

[sol invictus]

So there are black holes, black rings, and black holes with black rings?

Have black-rings ever appeared in nature? Have black holes with black rings appeared in nature?

They only exist in 4 (or more) spatial dimensions, so no.

How fast would the rotation of a black-ring be to keep it as a ring and not a black-hole?

I think there's a critical angular velocity (which probably depends on the mass), but I'd have to check. Actually if I recall well both can exist for some range of the parameters, but there will be one with more entropy, and so the other is probably unstable.

 

[INRM]

Sol Invictus,

From what you're saying, they can't exist in nature. So what's the point of hypothesizing about something that can't exist?

 

[sol invictus]

From what you're saying, they can't exist in nature. So what's the point of hypothesizing about something that can't exist?

Everyone does that all the time (ever read a novel? heard a political speech? watched a movie? learned about perfect circles?) - what's the problem?

In this case it's also interesting because

a) we don't know for sure there are only four dimensions, so they might actually exist,

b) sometimes studying abstract things gives you insight into concrete things,

c) there are very few exact solutions to Einstein's equations in any number of dimensions, and it's nice to have more,

d) seeing that this is possible in 5 dimensions helps us understand why it's not in 4,

e) etc.

 

[m_huber]

[Black Saturn]

Why is this not a band yet?