Kerr black hole in equilibrium with a rotating heat bath.

Abstract

The equilibrium and stability of a rotating black hole in a finite heat bath is discussed. An axisymmetric box of radiation in thermal equilibrium rotates rigidly, and some radiation slumps towards the outer wall. When such a heat bath is in equilibrium with a black hole, the temperatures and angular velocities of the hole and the bath are equal. The situation in which the heat bath is in a cylindrical box much larger than the hole, and contains only massless modes, is particularly simple and may be examined in detail. A sufficient condition for the stability of the equilibrium can be derived, analogous to the stability condition derived by Davies and by Gibbons and Perry for the nonrotating case. Depending on the total energy {ital E}, total angular momentum {ital J}, and radius {ital R} of the heat bath, the system at equilibrium may be in one of three thermodynamic regimes: a radiation-only state, a state dominated by a black hole, or a transition state in which both the black hole and the heat bath contain significant energy, angular momentum, and entropy.