SEMICLASSICAL BLACK-HOLE IN THERMAL-EQUILIBRIUM WITH A NONCONFORMAL SCALAR FIELD

Analytic semiclassical corrections to the Schwarzschild metric are fou nd perturbatively, to first order in epsilon = ($) over bar hM(2), for a quantized scalar held with arbitrary curvature coupling. The approx imation scheme developed by Anderson, Hiscock, and Samuel is used to p rovide approximate algebraic expressions for the components of the vac uum stress-energy tenser. The linearized Einstein equations are solved to find the metric perturbations caused by the quantized field. Micro canonical boundary conditions are imposed on a spherical wall enclosin g the black hole. The various physical effects of the back reaction, a nd their dependence on the value of the curvature coupling, are discus sed in detail. The perturbations are found most often to lower the tem perature of the black hole. Requiring that the entropy of the system b e increased by the quantized held results in upper and lower bounds on the value of the curvature coupling constant, -3.431 less than or equ al to xi less than or equal to 7/10.