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 (28)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• On Black Hole Entropy
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Near-horizon symmetries of extremal black holes
• Non-Supersymmetric Attractors
• Rotating Attractors
• Non-Supersymmetric Attractors in String Theory
• The Non-BPS Black Hole Attractor Equation
• The "physical process" version of the first law and the generalized second law for charged and rotating black holes
• Higher Derivative Corrections to Non-supersymmetric Extremal Black Holes in N=2 Supergravity
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Dirty black holes: Entropy versus area
• Stationary black holes and attractor mechanism
• First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories
• R^4 Corrections to D1D5p Black Hole Entropy from Entropy Function Formalism
• On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes
• Entropy Function for 4-Charge Extremal Black Holes in Type IIA Superstring Theory
• A Perturbative Method to solve fourth-order Gravity Field Equations
• Entropy Function for Non-Extremal Black Holes in String Theory
• Non-supersymmetric Attractors in Born-Infeld Black Holes with a Cosmological Constant
• 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
• Non-Supersymmetric Attractors in BI black holes
• Entropy function and higher derivative corrections to entropies in (anti-)de Sitter space
• Double Horizon Limit, AdS Geometry and Entropy Function

Cited by in corpus (2)

• Entropy function and higher derivative corrections to entropies in (anti-)de Sitter space
• More on entropy function formalism for non-extremal branes