Black-hole thermodynamics and renormalization

Ultraviolet regime in quantum theory with horizons, contrary to ordinary theory, depends on the temperature of the system due to additional surface divergences in the effective action. We evaluate their general one-loop structure paying attention to effects of the curvature of the space-time near the horizon. In particular, apart from the area term, the entropy of a black hole is shown to acquire a topological correction in the form of the integral curvature of the horizon. To get the entropy, heat capacity and other thermodynamical quantities finite, such a kind of singularities should be removed by renormalization of a number of constants in a surface functional introduced in the effective action at arbitrary temperature. We also discuss a discrepancy in the different regularization techniques.