Thermal interaction of a black hole with a finite temperature environment

Abstract

The evolution of the mass of a black hole in an environment with nonzero temperature is formulated and a preliminary qualitative analysis is undertaken. In particular, the absorption of heat is taken into account – a modification of the Hawking-Page estimate of black hole lifetimes. We deduce from thermodynamic arguments the instability of the equilibrium state. It is concluded that primordial black hole lifetimes are longer than those predicted by the rate equation dM/dt ∝ 1/M. We also present a short sketch of the thermodynamic approach (starting from entropy) to deriving the temperature, and equations of state of a black hole.