Horizon thermodynamics in $f(R,R^{\mu \nu }{R}_{\mu \nu })$ theory

Abstract

We investigate whether the new horizon first law still holds in $f(R,R^{\mu \nu }{R}_{\mu \nu })$ theory. For this complicated theory, we first determine the entropy of black hole via Wald method, then we derive the energy by using the new horizon first law, the degenerate Legendre transformation, and the gravitational field equations. For application, we consider the quadratic-curvature gravity and firstly calculate the entropy and the energy for a static spherically symmetric black hole, which reduces to the results obtained in literatures for a Schwarzschild-(A)dS black hole.

arXiv comment6 pages, no figures

References in corpus (29)

• Large N Field Theories, String Theory and Gravity
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Quantum Geometry and Black Hole Entropy
• The fuzzball proposal for black holes: an elementary review
• D-brane Approach to Black Hole Quantum Mechanics
• Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
• Energy in Generic Higher Curvature Gravity Theories
• Statistical interpretation of Bekenstein entropy for systems with a stretched horizon
• Gravitational Entropy and Global Structure
• Mechanism of Generation of Black Hole Entropy in Sakharov's Induced Gravity
• Quantum Black Holes: Entropy and Entanglement on the Horizon
• New Energy Definition for Higher Curvature Gravities
• The Bekenstein Formula and String Theory (N-brane Theory)
• Generalized Misner-Sharp Energy in f(R) Gravity
• Horizon thermodynamics in $f(R)$ theory
• On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions
• Black Hole Entropy from BMS Symmetry at the Horizon
• Noether Current, Horizon Virasoro Algebra and Entropy
• Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory
• Tolman mass, generalized surface gravity, and entropy bounds
• Evidence for an entropy bound from fundamentally discrete gravity
• Horizon Thermodynamics from Einstein's Equation of State
• Energy in Higher-Derivative Gravity via Topological Regularization
• Is gravity entropic force?
• Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor
• Horizon thermodynamics in fourth-order gravity
• Entropy and Energy of Static Spherically Symmetric Black Hole in $f(R)$ theory

Cited by in corpus (1)

• Thermodynamics of black hole in $D$-dimensional $f(R)$ theory