A-L-E-X wrote:Source of the post Intuitively, I had always thought that black holes were macro versions of quantum objects, which is why they seem to be singularities.

Eh, black holes don't have much to do with quantum mechanics. Their macroscopic properties are general relativistic almost all the way through and are also completely independent of a singularity at the center. (An argument could be made that quantum mechanics is important for understanding Hawking radiation, though it also has a lot to do with thermodynamics.)

If you want to see where quantum mechanics becomes manifest over macroscopic objects, then look at neutron stars. They are supported by neutron degeneracy pressure, which is a quantum mechanical effect arising from the Pauli exclusion principle (since neutrons are fermions and cannot occupy the same quantum state). Similarly for white dwarfs, supported by electron degeneracy pressure.

A-L-E-X wrote:Source of the post About relating the centrifugal force to rotating black holes, would that be a reason why the singularity might be a ring rather than a point?

It's hand-wavy, but you can think of it that way if you like.

To be more precise we need general relativity. When we derive the Kerr metric we actually start by putting all the mass at a

*point*at the coordinate r=0, just like we do for the Schwarzschild metric, but now we give it some angular momentum. Then we chug through the field equations and obtain the Kerr solution. Upon analyzing this solution, we find several singularities! The outermost one is the event horizon, and its singular nature can be found to simply be a consequence of the coordinates, rather than a place where the space-time is badly behaved. So it's a "coordinate singularity" that can be removed by switching to a more suitable coordinate system. Another coordinate singularity is found again at the inner event horizon. Finally when we look at the central singularity, we discover its location makes no sense. In polar coordinates it is satisfied at r=0 and a specific angle (θ=π/2), but

*not*at r=0 and any other angle. Yet those are the same point!

To resolve this we switch again to a new coordinate system, and find that the coordinate r=0 in the Kerr metric is actually describing a

*disk*(x

^{2}+ y

^{2}= a

^{2}), where a is the spin of the black hole. The specific angle where the singularity was satisfied (r=0, θ=π/2) describes a ring on the edge of that disk. This ring turns out to be non-removable by any other coordinate transformation. It's a true curvature singularity, where the space-time curvature is infinite, rather than a mere coordinate singularity. This is how the ring singularity of the Kerr metric was discovered -- and it wasn't trivial to find at all.

We must also remember though that this ring singularity is unphysical -- an artifact of the Kerr vacuum solution. Real rotating black holes do not contain them. Where the rotation of the Kerr metric does correspond to nature is in the shape of the event horizon, and the ergoregion where spacetime is dragged around so fast that an observer there cannot remain still.

A-L-E-X wrote:Source of the post Even without the Cauchy horizon, is a new space-time (that is, new universe) still possible once beyond the event horizon?

Probably not, despite how popular and appealing the idea is. But we don't really know. What we know with confidence is what happens near, through, and a fair ways below the event horizon. Near where the inner horizon or Cauchy horizon would be, our understanding breaks down.

I subscribe to the view that physics is always capable of describing "what happens" to something after some initial condition is provided, in principle. For a black hole interior, this means physics must not break down arbitrarily.

*Something happens*to a thing falling into a black hole. Its world line must be extendable to

*somewhere*. In classical general relativity, that somewhere terminates in a singularity (this is actually how singularities are defined: by the non-extendability of any world lines through it). A future theory of quantum gravity may replace the singularity with something very dense and exotic but not infinitesimal, where world lines still effectively terminate.

For a rotating black hole, we don't know where that termination point is. The vacuum solution predicts the world lines can be extended to another universe, but realistically we see many reasons why that should not be so. More likely it's some chaotic jumble of past and future near-singularities crashing into each other at relativistic speeds like the ultimate cosmic particle collider. To quote Andrew Hamilton, "what does nature do with such a machine?"

‾\_(ツ)_/‾