Black hole entropy, flat directions and higher derivatives

TL;DR

This paper investigates how higher derivative corrections affect extremal black hole entropy, especially in cases with flat directions and stability issues, using the entropy function formalism.

Contribution

It provides explicit formulas for entropy corrections due to higher derivatives and analyzes stability of black hole solutions with flat directions in a model-independent way.

Findings

Explicit correction formulas for black hole entropy with higher derivatives

Analysis of stability conditions for large and small black holes

Insights into the role of flat directions in black hole entropy and stability

Abstract

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point of view of small black holes and in the case when the classical black hole potential exhibits flat directions. A particular attention is paid to the issue of stability of several solutions, including large and small black holes by using properties of the Hessian matrix of the effective black hole potential. This is done by using a model independent expression for such matrix derived within the entropy function formalism.