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

TL;DR

This paper demonstrates that for small black holes with higher curvature corrections, the entropy is universally proportional to the horizon area, with a ratio of 1/2G, across various dimensions and correction types.

Contribution

It establishes a universal entropy-area relation for small black holes with higher curvature corrections using the entropy function formalism.

Findings

Entropy of small black holes is proportional to horizon area.

Universal ratio of entropy to area is 1/2G in many cases.

Relation holds across different dimensions and correction types.

Abstract

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy $S_{BH}$ of small black hole is proportional to its horizon area $A$. In particular we find a universal result that $S_{BH}=A/2G$, the ratio is two times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.