Can Colliding Stars Form a Black Hole Made of Light?

[A.T.]

If two stars, both slightly above their Schwarzschild radius collide, can a joint horizon form before they come in contact?

What if one is matter, and the other the same amount of antimatter? Will they annihilate each other completely to pure radiation, which stays within the horizon? Would there still be a singularity at the center?

 

[Dale]

If two stars, both slightly above their Schwarzschild radius collide, can a joint horizon form before they come in contact?

What if one is matter, and the other the same amount of antimatter? Will they annihilate each other completely to pure radiation, which stays within the horizon? Would there still be a singularity at the center?

If you have two stars above their Schwarzschild radius then the joint spacetime is no longer spherically symmetric, so the metric will be considerably more complicated than in the usual case. However, in principle they would collapse to form an EH that would not be perfectly spherically symmetric as long as the annihlation occurred after the matter and anti-matter were behind the horizon.

A less natural but easier to analyze situation would be a central sphere of matter surrounded by a collapsing spherical shell of antimatter. Since that is spherically symmetric you could "easily" solve the EFE. If the matter and anti-matter collide inside the horizon then the resulting EM radiation remains trapped.

 

[George Jones]

If two stars, both slightly above their Schwarzschild radius collide, can a joint horizon form before they come in contact?

Yes.

I believe that if you take several hundred million stars similar to the Sun (so each considered alone would be well outside its Schwarzschild radius) and congregate them such that they almost, but don't quite, touch, then the configuration will be inside its Schwarzschild radius.

 

[Bill_K]

I believe that if you take several hundred million stars similar to the Sun (so each considered alone would be well outside its Schwarzschild radius) and congregate them such that they almost, but don't quite, touch, then the configuration will be inside its Schwarzschild radius.

If that is the case, what is there to prevent it from undergoing a catastrophic collapse?

 

[Dale]

Nothing that we know of.

That is one of the most compelling arguments for the existence of event horizons, IMO. According to GR they can form at arbitrarly low densities if you have enough total mass.

 

[PAllen]

If some variants of the hoop conjecture are true, if two ordinary stars approaching each other at exceedingly near 2c (approach speed in COM frame), but not even on collision course, a BH will result, trapping them. This would happen if the ADM mass, which includes their KE, is sufficiently large, and closest approach is well within the hoop radius. Matter versus antimatter is completely irrelevant. Some form of singularity would result, but since the settled form of BH would be Kerr with extreme spin, the singularity would not resemble the spacelike SC singularity.

This would never happen for two nearby stars comoving per some observer.

 

[A.T.]

Thanks for the responses.

If that is the case, what is there to prevent it from undergoing a catastrophic collapse?

Yeah, for spherically symmetrical masses there is that 9/8Rs limit for stability. Everything below that must collapse. Does this not apply to low density, non-uniform mass distributions in space? Or are they always collapsing, once the horizon forms, just very slowly even for someone within the horizon?

 

[PAllen]

Thanks for the responses.



Yeah, for spherically symmetrical masses there is that 9/8Rs limit for stability. Everything below that must collapse. Does this not apply to low density, non-uniform mass distributions in space? Or are they always collapsing, once the horizon forms, just very slowly even for someone within the horizon?

Under broad assumptions, a singularity must form inside an EH, no matter how asymmetric or spinning. However, it is not known, even classically, whether (in a realist scenario) all mass ends up collapsed. It is known that the Kerr interior has essentially zero chance of forming because it is not stable against tiny perturbations. Nor is it known, even qualitatively, even classically, what is actually predicted by GR - it is just too complex. All that is known is some form of singularity occurs.

As an example of why it is plausible that not all matter ends up in the singularity, there are stable orbits inside a Kerr event horizon.

 

[bcrelling]

Nothing that we know of.

That is one of the most compelling arguments for the existence of event horizons, IMO. According to GR they can form at arbitrarly low densities if you have enough total mass.

The universe is at an arbitrarly low density but has not collapsed into a singularity despite having a great deal of mass.

Does this prove that the mass of the universe is finite?

 

[PeterDonis]

The universe is at an arbitrarly low density but has not collapsed into a singularity despite having a great deal of mass.

Does this prove that the mass of the universe is finite?

No, because the universe is expanding. What DaleSpam said, strictly speaking, only applies to a collection of objects that are all at rest relative to each other at some instant.

 

[Bill_K]

No, because the universe is expanding. What DaleSpam said, strictly speaking, only applies to a collection of objects that are all at rest relative to each other at some instant.

And if they are not at rest, there is a critical density (e.g. for the Friedmann universe ρ_c = 3H²/8πG) that marks the boundary line. For ρ < ρ_c collapse will not occur.