Entropy Function and Universality of Entropy-Area Relation for Small Black Holes

摘要

We discuss the entropy-area relation for the small black holes with highercurvature corrections by using the entropy function formalism and fieldredefinition method. We show that the entropy $S_{BH}$ of small black hole isproportional to its horizon area $A$. In particular we find a universal resultthat $S_{BH}=A/2G$, the ratio is two times of Bekenstein-Hawking entropy-areaformula in many cases of physical interest. In four dimensions, the universalrelation is always true irrespective of the coefficients of the higher-orderterms if the dilaton couplings are the same, which is the case for stringeffective theory, while in five dimensions, the relation again holdsirrespective of the overall coefficient if the higher-order corrections are inthe GB combination. We also discuss how this result generalizes to knownphysically interesting cases with Lovelock correction terms in variousdimensions, and possible implications of the universal relation.