Semiclassical black hole in thermal equilibrium with a nonconformal scalar field.

Abstract

Analytic semiclassical corrections to the Schwarzschild metric are found perturbatively, to first order in \ensuremath{\epsilon}=\ensuremath{\Elzxh}/${\mathit{M}}^{2}$, for a quantized scalar field with an arbitrary curvature coupling. The approximation scheme developed by Anderson, Hiscock, and Samuel is used to provide approximate algebraic expressions for the components of the vacuum stress-energy tensor. The linearized Einstein equations are solved to find the metric perturbations caused by the quantized field. Microcanonical boundary conditions are imposed on a spherical wall enclosing the black hole. The various physical effects of the back reaction, and their dependence on the value of the curvature coupling, are discussed in detail. The perturbations are found most often to lower the temperature of the black hole. Requiring that the entropy of the system be increased by the quantized field results in upper and lower bounds on the value of the curvature coupling constant, -3.431\ensuremath{\le}\ensuremath{\xi}\ensuremath{\le}7/10.