On one-loop renormalization of black-hole entropy

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 R2-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 contributions depending on the internal and external geometry of the horizon surface.