Entropy function and higher derivative corrections to entropies in (anti-)de Sitter space

TL;DR

This paper explores how the entropy function formalism can be used to efficiently compute higher-order corrections to the entropy of (anti-)de Sitter spaces and black holes, bypassing the need for metric corrections.

Contribution

It introduces a quick method to derive higher-order entropy corrections for (anti-)de Sitter spaces using an equation relating Sen's entropy function without requiring near horizon extremization.

Findings

Derived higher-order entropy corrections for (anti-)de Sitter spaces and black holes.

Showed that near horizon extremization is unnecessary for pure (anti-)de Sitter space.

Calculated entropy including Gauss-Bonnet, R^2, and R^4 terms.

Abstract

We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2$ terms and $R^4$ terms are calculated as concrete examples.