TEMPERATURE AND ENTROPY OF A QUANTUM BLACK BORE AND CONFORMAL ANOMALY

Attention is paid to the fact that the temperature of a classical black hole can be derived from the extremality condition of its free energy with respect to the variation of the mass of a hole. For a quantum Schwarzschild black hole evaporating massless particles the same condition is shown to result in the one-loop temperature T=(8πM)-1[1+σ(8πM2)-1] and entropy S=4πM2-σlnM expressed in terms of the effective mass M of a hole together with its radiation and the integral of the conformal anomaly σ that depends on the field species. Thus, in the given case quantum corrections to T and S turn out to be completely provided by the anomaly. When it is absent (σ=0), which happens in a number of supersymmetric models, the one-loop expressions of T and S preserve the classical form. On the other hand, if the anomaly is negative (σ<0) an evaporating quantum hole seems to cease to heat up when its mass reaches the Planck scales. © 1995 The American Physical Society.