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From my (somewhat limited) understanding of GR I know that there are two different kinds of solutions that produce a black hole, some that rotate and some that do not. What I can't figure out from my reading so far is which of the two is considered "typical" (if either). That is, when we think we have detected a black hole in space, do we initially suspect that it's rotating or stationary?

My naive assumption would be, since they form from collapsing rotating stars, that most black holes would continue rotating after formation, increasing in speed as they decreased in volume. However, I see a lot of discussion about black holes that use Schwarzschild's equations, which describes a non-rotating object. Is this merely because those are easier to deal with and "close enough", or is it really believed that many black holes are non-rotating?

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Rotating and nonrotating are linked continuously by making the angular momentum zero, so they aren't different kind of solutions, they are a parametrized family. The black holes we have observed for some reason are driven to not only rotate, but rotate very very fast, so that they are near the limit imposed by GR on angular momentum per unit mass. I remember reading recently that a typical galactic center black hole is rotating at 98% of extremality, which is ridiculous, but it seems to be true. Also, yes, the reason the discussions use Schwarzschild is because it's easier. –  Ron Maimon Jul 18 '12 at 1:59
    
If you could make that an answer and find a source for that observation that's exactly what I was looking for! –  Michael Edenfield Jul 18 '12 at 16:13
    
I understand, but I dug around, and I didn't find the source, and I am not sure about this craziness--- it's completely weird to have such an extremal hole. It was a few years ago, and it was big news in astro. –  Ron Maimon Jul 18 '12 at 16:21
    
@RonMaimon Check arxiv.org/abs/astro-ph/0612354 and arxiv.org/abs/astro-ph/0603813 –  mmc Jul 18 '12 at 16:35
    
Related: physics.stackexchange.com/q/12140/2451 –  Qmechanic Oct 4 '12 at 16:15
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1 Answer

Well, I have been working on Black Holes for nearly 3 years now. And you are partially right in assuming that rotating stars lead to rotating black holes. The actual dynamics is much more complex, as it is the core of the star which needs to have angular momentum after going hypernova.

Rotating black holes have a region around them, called the 'ergosphere'. In principle, we can extract energy from the ergosphere via a process called 'Penrose process'. And when we have extracted a maximum amount of energy, the black hole starts to lose its angular momentum, like a top, and soon comes to be non rotating.

Also, there are 4 solutions to the types of black holes. Not 2.

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Yes, sorry, that's my sloppy wording I think; there are two solutions that rotate and two that do not, correct? –  Michael Edenfield Jul 17 '12 at 22:50
    
That's the theoretical expectation, but observations of galactic center black holes show that they are at 98% of extremality regarding rotation! This is shocking if confirmed, I don't remember the source. –  Ron Maimon Jul 18 '12 at 1:58
    
When you say that there are 4 solutions, are you referring to charged/non-charged, rotating/non-rotating holes? –  magma Jul 19 '12 at 15:53
    
@RonMaimon: yes, but look at the rotational parameters for the sun. If it suddenly collapsed without shedding any matter, it would be super-extremal. Abhiram: what do you mean by four types of black holes? I believe carter's general static exact solution had five independent parameters, but the cosmological constant doesn't have much to do with the black hole, and I've never met anyone who expects astrophysical holes to have a Taub-NUT charge. –  Jerry Schirmer Oct 1 '12 at 21:31
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