What happens to the shrinking universe in the presence of the pressure of Hawking radiation? 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?
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.