Temperature and entropy of a quantum black hole and conformal anomaly

This is the authors' abstract. We don't add key points for this paper.

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=(8{π}M)^-1[1+{σ}(8{π}M²{)}^{{{-}}1}] and entropy S=4π{M}²$-{σ}lnM 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.