I’ve read many times that arrow of time can be explained from extremely low entropy of the Universe at the Big Bang (http://preposterousuniverse.com/eternitytohere/faq.html). The argument goes that initially the Universe was very smooth. As time passed, matter gathered together in clusters due to gravitation, until eventually we got stars, galaxies and super massive black holes.
There is a notion of entropy, related to gravitation. In classical statistical physics without taking into account gravity the gas spreads evenly in the volume. If gravity is taken into account than the most probable state of the system is when all gas forms a large black hole. However I don’t see how Hawking evaporation is taken into this picture. From this I conclude that somewhere there must be a textbook-level theory of entropy that takes into account gravity, Hawking radiation and expansion of the Universe.
In general, we may consider a toy model – the Universe, consisting entirely of black holes of different sizes and velocities, see how it evolves and get the most probable state (or states).
If the Universe contained only black holes with a certain mass and velocity distribution, how would it evolve over time? Is it enough to know the mass/velocity distribution to predict the general evolution of such Universe? Is it possible to predict the spectrum of background radiation in such a Universe at any moment of time?