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Black holes release Hawking radiation. Now assume that the universe after all collapses back again, bringing all matter to a single black hole. I assume that this would bend the whole space-time of the universe as well, wrapping it around the black hole.

Now what happens to the shrinking universe in the presence of the pressure of Hawking radiation?

Could there be a stable point where pressure and gravity are balanced?

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In a shrinking, roughly 3-spherical universe with only a black hole, Hawking radiation should follow a geodesic line and return to the black hole, without excerting radiation pressure to the universe as a whole.

Therefore it's hard to see, how Hawking radiation should establish an equilibrium with gravity.

More feasible seems, that the shrinking universe can prevent the black hole from further evaporation at some point, since evaporated particles and radiation are directed back into the black hole by the overall curvature of spacetime.

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I thought that the Heisenberg uncertainty principle would force some quantum effects, like particle radiation, and thereby produce a certain pressure to whatever... –  draks ... Feb 23 '14 at 22:14
The Hawking radiation can be seen as a consequence of the Heisenberg uncertainty. But where can the radiation act on to excert a pressure? There is only the black hole. The overall radiation pressure to the black hole is cancelling out by the symmetry of the constellation. –  Gerald Feb 23 '14 at 22:20
Let's assume that the black hole's radiation starts at one and returns to the other end of the hole. What if there is some kind of Casimir effect between the two parts of the event horizon? –  draks ... Feb 24 '14 at 23:33
The Casimir effect is negligible in voids of a macroscopic scale. To be strong enough to warp spacetime in a relevant way, we would either have to look to event horizons close to the Planck scale, or need a huge amount of layered lamellae (to get a relevant Casimir effect in the narrow gaps between the lamellae) near a macroscopic event horizon. –  Gerald Feb 26 '14 at 12:59
Gerald, thanks (+1) so far, I gotta think about it... –  draks ... Feb 27 '14 at 6:51

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