On black hole thermodynamics and the entropy function formalism

Abstract

From the black hole thermodynamics point of view, we show that the entropy function $\mathbf{f}$ and the free energy $F$ are related via $\mathbf{f}=e_I{q}_I+{\Omega }_H{q}_I{A_{\varphi }^I}^{\prime }-\frac{\partial F}{\partial r}{|}_{r_H}$. Assuming the entropy function is known for extremal black holes, we propose an approach to calculate the entropy of non-extremal cases by slightly moving the extremal black hole geometry from extremality. The entropy of non-extremal $D1D5$- and $D1D5p$-branes in the presence of higher derivative corrections are computed as concrete examples. An attempt has also been made to explain why the entropy function method can calculate the corrected entropy without knowing the exact form of black hole solution in higher derivative gravity theories.

18 pages, contents improved, typos corrected, references added

References in corpus (6)

• Near-horizon symmetries of extremal black holes
• Stationary black holes and attractor mechanism
• On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes
• Entropy Function and Universality of Entropy-Area Relation for Small Black Holes
• Euclidean analysis of the entropy functional formalism
• Double Horizon Limit, AdS Geometry and Entropy Function