Rotating Black Holes: A Century of Discovery & Beyond

[snorkack]

Schwarzschild black holes were discovered over 100 years ago, in 1915.
Quite soon, in a couple years (by 1916...1918), charged Reissner-Nordström holes were discovered.
Yet rotating black holes were only discovered by Kerr in 1963 - 48 years after Schwarzschild holes.
Why? What was known about rotating black holes through the 48 years in the meantime, in 1920s to 1950s?

Also, while rotating and charged, Newman holes were discovered by 1965, Kerr and Newman holes are axisymmetric.
What, if anything, is known about rotating black holes with non-axisymmetric interior?

 

[PeterDonis]

What was known about rotating black holes through the 48 years in the meantime, in 1920s to 1950s?

Nothing, really. Even when Kerr discovered his solution, it wasn't immediately realized that it described a rotating black hole; at first it was thought that it described the vacuum region around a rotating star or planet. People had been searching for such a solution for some time but had been unable to find one--and once it was realized that Kerr's solution described a rotating black hole, it turned out that the spacetime outside a rotating star is not necessarily described by Kerr's solution. In other words, for rotating bodies there is no analogue of Birkhoff's theorem, which says that the vacuum region outside any spherically symmetric non-rotating body is described by the Schwarzschild solution.

What, if anything, is known about rotating black holes with non-axisymmetric interior?

Nothing, if you mean exact solutions. I believe numerical simulations have been done of this case, but I don't have any references handy.

 

[phyzguy]

Numerical solutions and analytic analysis (see this paper, for example) show that a rotating, non-axisymmetric black hole relaxes to an axisymmetric Kerr solution very rapidly. The relaxation time is on the order of $\tau \approx \frac{\hbar}{\pi k T}$, where T is the BH temperature. This reduces to $\tau \approx \frac{8 G M}{c^3}$. For a 50 solar mass black hole, this is a few milliseconds. This relaxation is referred to as the "ring-down" phase in the GW papers. Since they relax to the Kerr solution so quickly, I think this is why most people focus on the Kerr solution.

 

[pervect]

For the interior structure, there are some papers by Hamilton. See for example https://arxiv.org/abs/1010.1272 , companion papers, and other papers by the same author on the topic. I don't believe the question is settled by any means, but there has been some work done.

 

[PeterDonis]

Numerical solutions and analytic analysis (see this paper, for example) show that a rotating, non-axisymmetric black hole relaxes to an axisymmetric Kerr solution very rapidly.

This applies to the region outside the horizon; but the OP is asking about the interior, inside the horizon. The "no hair" conjecture, which is what these simulations essentially confirm, only applies to the exterior. The Kerr interior is known to be unstable against small perturbations, so I would not expect a non-axisymmetric hole's interior to relax to a Kerr interior (although its boundary, the horizon, would relax to a Kerr horizon, as the simulations show).

 

[phyzguy]

This applies to the region outside the horizon; but the OP is asking about the interior, inside the horizon. The "no hair" conjecture, which is what these simulations essentially confirm, only applies to the exterior. The Kerr interior is known to be unstable against small perturbations, so I would not expect a non-axisymmetric hole's interior to relax to a Kerr interior (although its boundary, the horizon, would relax to a Kerr horizon, as the simulations show).

Good point. Since we can never access the interior, aren't discussions of what is inside the horizon somewhat philosophical? Or do you think simulations may be able to someday give information about the interior?

 

[PeterDonis]

Since we can never access the interior, aren't discussions of what is inside the horizon somewhat philosophical?

No, because we can still use our best understanding of the laws of physics to predict what happens in the interior.

Or do you think simulations may be able to someday give information about the interior?

Yes.

 

[snorkack]

So the Hamilton theory, as set out by https://arxiv.org/pdf/1010.1269.pdf in 2012
but not universally accepted as of 2017
is that a rotating black hole interior has an axisymmetric and stable structure different from the Kerr one?