Similarities and differences Black Holes and Big Bang

[Gerinski]

I know that likening Black Holes to the Big Bang is common among laymen and that scientifically educated people quickly reply that they are completely different things. But I would like to understand better in which aspects are they similar and in which they are different.

If we run the universe backwards, we get to a point beyond the CMB where matter ceases to exist as such, it all gets so hot that even the quark-gluon plasma and the radiation fuses into some sort of "primeval energy" where particles are not yet formed, and the different forces get unified, possibly also gravity just a tiny instant after the BB. Let's forget the singularity itself, but at that tiny instant after the BB, all forces are possibly unified, spacetime is tiny, and all the energy is confined in that spacetime volume with an inconceivably high density.

In a Black Hole, the matter-radiation falling into it also gets increasingly condensed into an ever smaller volume. Again, let's forget about the singularity itself, let's just go a point very close to reaching the singularity status.
The energy density gets also incredibly huge. But, do other analogies hold?

The confinement of all the mass-energy in such as small volume, does it mean that the center of the black hole must be a very hot place? May the matter-energy become a "quark-gluon plasma plus radiation" near the center, and just "primeval energy" even closer to the very center?

Can we assume that the different forces also get unified as we get closer to the center of the black hole?

We surely feel the gravity of the black hole. Perhaps that would mean that gravity does not actually unify with the other forces even at near-singularity conditions?

Could we say that "time runs backwards" beyond the event horizon and towards the hypothetical singularity?In summary, here I have proposed some questions, but in general I'm interested in getting to know better in which respects are Black Holes and Big Bangs similar or different, seen as possibly reverse manifestations of a same concept, i.e. energy emerging from (hypothetically) infinite density into a growing spacetime as time moves forward, vs energy compressing into (hypothetically) infinite density into a shrinking spacetime as time moves (in principle) forward.

 

[PeterDonis]

I would like to understand better in which aspects are they similar and in which they are different.

The short answer: they are simliar in that both spacetimes have a curvature singularity which is spacelike ("curvature singularity" means that spacetime curvature increases without bound as the singularity is approached). They are different in all other respects.

The confinement of all the mass-energy in such as small volume, does it mean that the center of the black hole must be a very hot place?

Not after it's formed. In the process of forming a black hole, the collapsing matter behaves (at least in the simplest model) like a time reverse of the Big Bang--it increases in density and temperature as it collapses, so yes, it would switch states from ordinary matter to plasma to quark-gluon plasma to whatever comes before that. But once the hole is formed and the singularity appears (again, in the simplest model), all that matter has vanished and the interior of the hole is vacuum.

Matter can still fall into the hole, but it will get torn apart by tidal gravity as it approaches the singularity; in other words, matter that falls into an already formed hole undergoes a different process than the matter that formed it. So the interior of an already formed black hole is not a hot, dense place like the early universe.

Can we assume that the different forces also get unified as we get closer to the center of the black hole?

No, because unification of the forces requires a hot, dense place like the early universe, and the interior of an already formed hole isn't such a place. See above.

We surely feel the gravity of the black hole. Perhaps that would mean that gravity does not actually unify with the other forces even at near-singularity conditions?

It doesn't say anything either way. The gravity you feel does not come from inside the hole; it comes from the collapsing matter that originally formed the hole. See here:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

Could we say that "time runs backwards" beyond the event horizon and towards the hypothetical singularity?

No.

Note: All of the above is according to the classical model of black holes, in which there is a genuine curvature singularity inside the hole. Quantum effects might change that (in fact, the majority opinion among physicists seems to be that they will). But we don't have a theory of quantum gravity, so we can't really say what a "correct" quantum model of a black hole's interior looks like. However, the same caveat applies to the early universe: the model in which there is a singularity at the beginning is the classical model, and quantum effects might change that, but we don't know exactly how. So in the above I have stuck to the classical model in both cases (black hole and early universe), since that's what you appeared to be basing your question on.