On one-loop renormalization of black-hole entropy

Abstract

One-loop divergences appearing in the entropy of a quantum black hole are proven to be completely eliminated by the standard renormalization of both the gravitational constant and other coefficients by the $R^2$-terms in the effective gravitational action. The essential point of the proof is that due to the higher order curvature terms the entropy differs from the Bekenstein-Hawking one in the Einstein gravity by the contributions depending on the internal and external geometry of the horizon surface.

10 pages, latex, no figures; The text is slightly changed and some new eqs. are added to make the proof of our statement more transparent. This version will appear in Phys. Lett. B

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