Does the formation of a black hole start with QM?

[superpaul3000]

Most people on this forum know the basic theory of black hole formation. When a massive star runs out of fuel there is no longer enough heat pressure pushing out against the gravity pulling in and the star collapses. The density of the core and resulting remnant become so large that nothing, not even light, can escape. This forms an event horizon and something we call a black hole.

However, I have not found much more information than that. I was curious as to the details of what is going on at the core of the collapse in the formation of the black hole. I tried to understand this process with the known laws of physics. This of course means one must consider QM in the picture.

So QM predicts that there is some non-zero vacuum energy randomly producing virtual particles that are continuously created and then annihilate with each other. It is also possible that microscopic black holes form from these quantum fluctuations but since they are so small they evaporate through hawking radiation very quickly. These mini black holes are forming all around us all the time and presumably also forming at the cores of collapsing stars. So my understanding would be that given a critical density of matter, one which could be realized during this collapse, the mini black hole gets close enough to particles of matter to suck them into it. The bigger it gets the slower it evaporates and the faster it grows. The final result is a supernova with a black hole remnant at its center.

Is this an existing theory of black hole formation? Are there other theories that describe the details of black hole formation?

 

[mathman]

The existing theory of black hole formation does not start with a microscopic black hole. The essential point is that quantum effects are no longer strong enough to counter gravity so that the collapsing star remnant (if it is massive enough) has a small enough volume so that the escape velocity is greater than the speed of light.

 

[stevebd1]

I think some insight can be gained from looking at the Schwarzschild interior metric. If we consider the time component only-

$$d\tau=\left( \frac{3}{2}\sqrt{1-\frac{2M}{r_0}}-\frac{1}{2}\sqrt{1-\frac{2Mr^{2}}{r_0^{3}}}\right)dt$$

where r₀ is the radius of the spherical mass. If we consider a neutron star that has just exceeded the TOV limit at 3 sol mass through accretion, r₀ will gradually reduce. Considering M being a constant and r₀ reducing, when r₀ reaches 9M/4, $d\tau$ at r=0 (i.e. the centre of the neutron star) becomes zero. As r₀ becomes less than 9M/4, a radius where $d\tau=0$ begins to move outwards from the centre, any volume of space within this radius is spacelike and because there are no stable radii in spacelike spacetime, this will induce the collapse of matter within to a form of singularity. This radius where $d\tau=0$ will continue to move outwards as r₀ reduces until they both meet at 2M and the interior solution becomes the vacuum solution.

 

[Naty1]

The existing theory of black hole formation does not start with a microscopic black hole. The essential point is that quantum effects are no longer strong enough to counter gravity..

I think that's correct.

Does the formation of a black hole start with QM?

a bit more detail:

yes. Essentially when a mass of sufficient size (say a star) begins to compact, as when nuclear reactions subside, the gravitational attraction of the mass begins to confine electrons and electron degeneracy pressure opposes (fights) the collapse...if mass is sufficient, the electron "cloud" collapses and even neutron and proton degeneracy pressure in the nucleus of the matter cannot oppose sufficiently strong gravity...everything is "crushed" and the matter destroyed as a singularity is formed...

Try wikipedia for "degeneracy pressure"...A great book with probably 50 or more pages discussing this specific phenomena is Kip Thorne's BLACK HOLES AND TIME WARPS...find a used paperback cheap...no complex math, lots of physical insights and explanations...

However, here is no complete theory of quantum gravity yet, combining QM and GR, so there are still issues to resolve...

 

[superpaul3000]

I talked to Martin Bojowald today seeing as he would have some knowledge in the matter. I think stevebd1 was getting at the same thing. It's not that the black hole forms as a point at the center of a collapsing star, but rather when some spherical region of space centered at the core has enough mass within it, its surface becomes an event horizon. If this event horizon formed inside a feeding neutron star, an outside observer would see the surface of the neutron star become more and more red shifted at a slower and slower rate until it appeared to be a black hole. I find it kind of fascinating that even though at the center of the collapse there is zero gravity due to vectors canceling out, the matter still can have a black hole forming around it.

I guess that is what I was looking for in terms of what the current theory is. I'm still not entirely convinced that it is what is really happening. That model predicts a singularity at the center of the black hole which is problematic. I think the theory with mini black holes could avoid a singularity and avoid the information loss paradox.

 

[Naty1]

I think stevebd1 was getting at the same thing. It's not that the black hole forms as a point at the center of a collapsing star, but rather when some spherical region of space centered at the core has enough mass within it, its surface becomes an event horizon.

I'm not sure just what point you make.

The absolute horizon forms at the singularity then spreads smoothly to the instantaneously appearing relative horizon ..at the critical circumference.


Here is how Kip Thorne describes the singularity...

The object the center of black hole... is the region where gravity becomes infinitely strong causing the laws of physics as we know them to break down...The Schwarzschild "singularity" ...is the critical circumference is nothing but a klocation where things can fall but out of which nothing can come...which Rindler gave the critical circumference a new name...the horizon.

and on page 477 somehting I did not remember:

In the singularity the laws of quantum gravity destroy time, leaving space alone and vulnerable...and the laws of quantum gravity then convert space into a random probabilistic foam...in the froth, space does not have any definite shape (that is, any definite curvature, or even any definite topology). Instead space has various probabilities for this, that or another curvature and topology.