Black holes & expanding universe

[ifarcas]

Hello everyone. I'm a beginner with questions

Can someone tell me what happens with black holes in an expanding universe? If the fabric of the universe is expanding wouldn't this result into weaker interactions inside the black hole up to the point when the black hole cannot hold the matter togeder? Wouldn't this result into a big explosion caused by interparticle forces overcoming the gravitational force? If so then wouldn't this contradict the idea that nothing escapes a black hole?

Thank you.

 

[Oxymoron]

Black holes do not hold matter together, and there is probably no matter interaction inside a black hole. In fact nobody knows what happens to matter once it crosses the event horizon. So we certainly do not know what happens inside a black hole regardless of the expanding universe.

Besides, the expanding universe should have no effects on the interior dynamics of a black hole, just as the expanding universe has no effect on us or anything else.

 

[Oxymoron]

On second thoughts, isn't there a thing as "gravitational memory"? If there is then surely the Black hole "remembers" it's effective gravitational constant at the instant it forms? Then it must remain constant at it's surface as it evolves in time. This would result in some strange things happening.

On the other hand, if the the grav. constant changes with time, then it must do so as to compensate for the expanding universe such that the size of the Black Hole can always be approximated by the formula R = 2GM. I think this sounds like a better explanation. But I am not sure if I can simply rule out that thing called "gravitational memory" (if it exists at all! Maybe someone can help there).

This is an interesting question though (modified): "What happens to a Black Hole in an expanding universe". Forget about the matter interaction and explosions and contradicting the fact that nothing escapes a Black hole and stuff; because it would not be a Black Hole if matter could exit it, would it!?

 

[ifarcas]

"because it would not be a Black Hole if matter could exit it, would it!?"

Yes this is exactly what I'm wondering myself. I can't see how a black hole could survive in an expanding universe (http://en.wikipedia.org/wiki/Big_Rip). IMHO black holes and Big Rip seem to be mutually exclusive. Or I'm missing something (beside knowledge )?

 

[pervect]

At the most basic level, it might help to read and appreciate Ned Wright's cosmology faq

Why doesn't the solar system expand if the whole universe is expanding

On a more advanced level, black holes in an expanding space-time can be represented by the Schwarzscild de-Sitter metric.

http://arxiv.org/abs/gr-qc/0602002

if one goes to the limit of large times, corresponding to a low matter density, i.e. the "end stage" of an expanding universe where the matter density in free space is negligible.

One way of approaching the problem is to calculate the horizon from the resulting metric.

The horizon is located where the metric coefficient for time goes to zero. This traps photons as well, as can be seen if one knows about null geodesics. Photons always have an invariant interval dx^2 - c^2 dt^2 = 0 (in geometric units, used in this paper, dx^2 - dt^2 = 0).

This means that when the metric coefficient g00 goes to zero, one has the position of the horizon. (One can also have a horizon if g11 becomes infinite, but that doesn't apply in this case)

In schwarzschild geometry, this occurs when 1-2m/r = 0, i.e. when r=2m, which is the correct location for the horizon.

In the Schwarzschild de-Sitter geometry, this occurs when 1 - 2m/r - Lambda/r^2 = 0

where Labda is the cosmological constant of the de-Sitteer space-time. So it can be seen that there is no problem with black holes existing in a de-Sitter spacetime. The event horizon gets shifted a bit, that's the only effect.

Another way of approaching the problem is to realize that de-Sitter space is actually static, i.e. time invariant, if the proper coordinates are used. This is mentioned in the Wikipedia article on de-Sitter space (which is rather technical), and the original coordinates that de-Sitter used were in this form.

If one has a FRW expanding universe with matter present, the details will be more compex, due to the presence of matter as well as a cosmological constant. Some of the matter will fall into the black hole, some at a far enough distance will escape, making the initial problem dynamic. As time evolved, though, it will eventually settle down to a static solution. One complicating factor may arise if the black hole mass does not remain fninite. I think I recall reading about such concerns somewhere, by Baez, but I don't recall the details. If one assumes this doesn't happen, the result is fairly simple, a static black hole in a static Schwarzschild de-Sitter spacetime.