B Why does anyone think gravity might collapse wave function?

[Demystifier]

A white hole "formation" is not possible because a white hole contains an initial singularity--there can't be anything "before" it, by definition. If there is, it's not a white hole.

Not exactly. The definition of black or white hole involves the existence of future or past event horizon. The singularity is not a part of the definition of black or white hole. Instead, the singularity is a result of a theorem, which assumes an energy condition. So if energy condition is not assumed, it is possible to have a black or white hole without singularity.

 

[PeterDonis]

The definition of black or white hole involves the existence of future or past event horizon.

Yes, that's true; a better statement of the required initial condition for a white hole would be that a past horizon has to exist. But a past horizon also can't be brought into being (i.e., there can't be anything "to the past" of it--in more technical terms, it must go all the way back to past timelike infinity), so white hole formation is still ruled out.

the singularity is a result of a theorem, which assumes an energy condition.

Yes, but note that the theorem does not connect a singularity with an event horizon. It connects a singularity with a trapped surface. They're not the same in general, although they happen to coincide in the idealized case of maximally extended Schwarzschild spacetime.

if energy condition is not assumed, it is possible to have a black or white hole without singularity.

No, if the energy condition is not assumed, it is possible to have a trapped surface without a singularity. But this tells us nothing about whether or not it is possible to have a black or white hole without a singularity, since those are defined in terms of event horizons, not trapped surfaces.

 

[Demystifier]

No, if the energy condition is not assumed, it is possible to have a trapped surface without a singularity. But this tells us nothing about whether or not it is possible to have an event horizon without a singularity.

Maybe the theorem itself does not imply it, but explicit black hole solutions (such as the Bardeen black hole) without singularity are known when energy condition is not required. The simplest way to construct such a solution is to write down by hand a regular black hole metric that you want, compute the Einstein tensor for that metric, a finally use the Einstein equation to find the needed energy-momentum tensor.

 

[PeterDonis]

the Bardeen black hole

Do you mean the metric described in equation (1) of this paper?

https://arxiv.org/abs/2007.09408

 

[Demystifier]

Do you mean the metric described in equation (1) of this paper?

https://arxiv.org/abs/2007.09408

Yes.

 

[PeterDonis]

the Bardeen black hole

From what I can gather, the maximal extension of this looks like Reissner-Nordstrom, the only difference being that there is just a regular timelike line at $r = 0$ instead of a timelike singularity. However, $r = 0$ is still behind a Cauchy horizon, meaning that this idealized solution is probably not physically realizable for the same reason as Reissner-Nordstrom is not: the Cauchy horizon (inner horizon) is unstable against small perturbations and would probably be replaced by something spacelike, looking more like the $r = 0$ singularity in Schwarzschild. Ultimately all this probably won't get resolved unless and until we have a confirmed theory of quantum gravity.

 

[PeterDonis]

From what I can gather, the maximal extension of this looks like Reissner-Nordstrom, the only difference being that there is just a regular timelike line at $r = 0$ instead of a timelike singularity. However, $r = 0$ is still behind a Cauchy horizon

To expand on this somewhat, based on some numerical investigations I have been making (and on what is said in some other papers I have found), there is a critical value of $g$ at which the horizon is degenerate (outer and inner horizons merge). For smaller values of $g$, there are two horizons and what I said in the quote above applies. The degenerate case corresponds to the similar case with Reissner-Nordstrom. For larger values of $g$, there is no horizon at all; this corresponds to the "naked singularity" case of Reissner-Nordstrom, but there is no singularity at $r = 0$ so this case corresponds to a static object that is supported against gravity by a sort of "magnetic repulsion" near the center.

 

[Demystifier]

To expand on this somewhat ...

Since you seem to be very interested in this stuff, here are some more papers you might be interested in.
https://arxiv.org/abs/gr-qc/0506126
https://arxiv.org/abs/1911.01020

 

[PeterDonis]

Since you seem to be very interested in this stuff, here are some more papers you might be interested in.
https://arxiv.org/abs/gr-qc/0506126
https://arxiv.org/abs/1911.01020

Thanks! These look interesting.

 

[PeterDonis]

https://arxiv.org/abs/gr-qc/0506126

The Penrose diagram in Fig. 5 of this paper is very interesting. What it is saying is, if you include evaporation in your model as well as formation, there is no true black hole any more. That is, there is no region of spacetime that cannot send light signals to future null infinity, and thus no event horizon (which would be the boundary of such a region).

Another way of putting this is that this paper gives a "semi-classical" model of how gravitational collapse would work in the presence of quantum fields that, when "compressed" enough, can violate energy conditions (and we already know quantum fields can do that) and thereby evade the conclusions of the singularity theorems and have regions of spacetime containing trapped surfaces without having a singularity. It also neatly avoids the issues involved with the inner (Cauchy) horizon in the non-evaporating case (illustrated in Fig. 1 of this paper, which matches the description I gave in post #56).

As the paper notes (p. 4, second paragraph in right column), this thing still looks like a black hole to outside observers, since stuff falls into it and doesn't come out for a time comparable to the Hawking radiation time (something like $10^{70}$ years for a mass of 10 solar masses), and the light from infalling objects gets redshifted by unbounded amounts as the objects approach the outer trapping horizon (which "looks like" an event horizon for a very long time, even though, considering the full spacetime, it isn't).

A key question that this paper doesn't mention is what a merger of two of these things would look like in terms of gravitational wave emission. Would it look similar enough to the waveforms LIGO has detected?