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

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.

24 pages, contents improved, typos corrected, references added

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• Intersecting Attractors
• Near horizon data and physical charges of extremal AdS black holes
• alpha'-corrections and heterotic black holes
• Lorentzian Robin Universe of Gauss-Bonnet Gravity
• On black hole thermodynamics and the entropy function formalism
• More on entropy function formalism for non-extremal branes