The evolution of black holes in an expanding universe

We examine the cosmological evolution of black holes in an expanding universe, taking into account the process of Hawking evaporation and including the influence of the black holes on the expansion dynamics. The black holes are assumed to have a mass spectrum of power-law form. We find analytic solutions in which the energy density in black holes is in equilibrium with radiation (though no individual black hole is), and demonstrate that they are attractors for the system. We study the approach to this attractor. For a matter-dominated era, we find the general solution for black hole evolution, and again demonstrate an attractor property. Some consequences of this analysis for the study of the early universe are discussed.