A simple Black Hole question I can't find an answer for

[PeterDonis]

Is this a consequence of the No Hair Theorem?

No, it's a consequence of looking at the mathematical formula for the invariant and seeing that there is a factor of $r^6$ in the denominator.

The No Hair Theorem has nothing to do with the singularity. It's about what properties of a black hole are observable from the outside.

 

[PeterDonis]

Is the BKL singularity generally accepted as being the likely framework for an interior black hole solution nowadays?

AFAIK, yes, it seems to be a good general description of what shows up in simulations.

 

[PeterDonis]

infinite (and in the BKL case, chaotic) tidal forces ripping everything apart (I presume this would even include atoms, though I haven't seen any such calculations) happens before the singularity,

No, finite but very, very large tidal gravity happens before the singularity. Not "infinite"; that only happens in the limit of reaching the singularity (which is not actually part of the spacetime). And the arguments for GR breaking down all involve it breaking down at some finite, but very, very large, curvature (such as the Planck scale). So it would break down somewhere before the singularity. The question is, how much before, as compared with when various kinds of objects get torn apart?

 

[Matterwave]

No, it's a consequence of looking at the mathematical formula for the invariant and seeing that there is a factor of $r^6$ in the denominator.

The No Hair Theorem has nothing to do with the singularity. It's about what properties of a black hole are observable from the outside.

I meant my question for the statement "which AFAIK is all black hole solutions."

 

[PeterDonis]

I meant my question for the statement "which AFAIK is all black hole solutions."

The answer is still the same: the No Hair Theorem has nothing to do with what happens to curvature invariants as the singularity is approached. You have to look at the actual formulas for the invariants.

 

[Matterwave]

Right... I'm not talking about scalar invariants or singularities in my latest question. I understand the scalar invariants in Kerr-Newman black holes go to infinity as you approach the "center" r=0 as a power of 6.

I thought you said Kerr-Newman black holes encompass all Black Hole solutions (lmk if I read you wrong). Those are the solutions that describe black holes with mass, charge and angular momentum. So, are you making that statement because the No hair theorem?

 

[PeterDonis]

I thought you said Kerr-Newman black holes encompass all Black Hole solutions

More precisely, they encompass all vacuum (actually electrovacuum, see below) black hole solutions. The Vaidya metric was mentioned earlier; that's a non-vacuum solution that also has an event horizon and a singularity, so it could be termed a "black hole". Some sources are stricter about terminology and only include vacuum solutions in the term "black hole".

Those are the solutions that describe black holes with mass, charge and angular momentum.

Vacuum solutions, yes. (Actually, "electrovacuum" is more accurate, since we're allowing charge to be present, but no other stress-energy besides the EM field associated with the charge. In other words, we are looking at solutions of the Einstein-Maxwell Equations with no other stress-energy present.)

So, are you making that statement because the No hair theorem?

Making what statement? That the Kerr-Newman family of black holes is all vacuum black hole solutions? Yes, that statement is believed to be true because of the no hair conjecture (I say "conjecture" because AFAIK there is still no general proof of it that covers all cases). See Wald, Section 12.3, for an outline of the reasoning.

 

[martinbn]

More precisely, they encompass all vacuum (actually electrovacuum, see below) black hole solutions.

What about space-times with multiple blackholes?

 

[Matterwave]

More precisely, they encompass all vacuum (actually electrovacuum, see below) black hole solutions. The Vaidya metric was mentioned earlier; that's a non-vacuum solution that also has an event horizon and a singularity, so it could be termed a "black hole". Some sources are stricter about terminology and only include vacuum solutions in the term "black hole".


Vacuum solutions, yes. (Actually, "electrovacuum" is more accurate, since we're allowing charge to be present, but no other stress-energy besides the EM field associated with the charge. In other words, we are looking at solutions of the Einstein-Maxwell Equations with no other stress-energy present.)


Making what statement? That the Kerr-Newman family of black holes is all vacuum black hole solutions? Yes, that statement is believed to be true because of the no hair conjecture (I say "conjecture" because AFAIK there is still no general proof of it that covers all cases). See Wald, Section 12.3, for an outline of the reasoning.

Got it, thanks! I'll take a deeper read of 12.3. I skimmed through it earlier.

 

[PeterDonis]

What about space-times with multiple blackholes?

There aren't any, at least not with the usual definition of "black hole". An asymptotically flat spacetime can only have one region that can't send light signals to infinity. You can have spacetimes with what look like multiple black holes, but they must always merge eventually into a single one, which means that the black hole region of the spacetime is actually just one connected region--but shaped, heuristically, like a pair of trousers instead of a cylinder (or trousers with more than two legs if more than two holes merge).

Schwarzschild-de Sitter spacetime does, in its maximal analytic extension, have more than one "black hole" region, that can't send light signals to its corresponding cosmological horizon. But there are also multiple cosmological horizons, so this spacetime, heuristically, can still only have one black hole per "universe" (region inside a particular cosmological horizon). This spacetime is not asymptotically flat, so there is no "infinity" to not be able to send light signals to, so it doesn't meet the standard definition of a black hole. (The presence of the positive cosmological constant changes the global structure.)