Noether Charge and Black Hole Entropy in Modified Theories of Gravity

Abstract

The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole is one-quarter of the horizon area in f(R) theories coupled to conformally invariant matter. If matter is present that is not conformally invariant the entropy is still proportional to the area of the black hole, but the coefficient is generally not one-quarter. The entropy of black holes in generalized dilaton theories and in theories with Lagrangians that depend on an arbitrary function of the Ricci tensor are also examined.

Changes to sections 3 and 4 plus minor changes, 10 pages

References in corpus (59)

• Black Hole Entropy is Noether Charge
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Can modified gravity explain accelerated cosmic expansion?
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• On Black Hole Entropy
• The Cosmology of Generalized Modified Gravity Models
• Curvature quintessence matched with observational data
• Are f(R) dark energy models cosmologically viable ?
• Reconciling dark energy models with f(R) theories
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• One-loop f(R) gravity in de Sitter universe
• Modified gravity with $\ln R$ terms and cosmic acceleration
• Where new gravitational physics comes from: M-theory?
• Observational constraints on dark energy with generalized equations of state
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Thermodynamic Behavior of Field Equations for f(R) Gravity
• Cosmological dynamics of R^n gravity
• Accelerated Cosmological Models in Ricci squared Gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• Cosmological perturbations in the Palatini formulation of modified gravity
• Entropy and universality of Cardy-Verlinde formula in dark energy universe
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• Increase of Black Hole Entropy in Higher Curvature Gravity
• The matter power spectrum in f(R) gravity
• The Universality of Einstein Equations
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Cosmological Constraints on f(R) Acceleration Models
• Modified-Source Gravity and Cosmological Structure Formation
• The Newtonian limit at intermediate energies
• Dirty black holes: Entropy as a surface term
• Accelerated Cosmological Models in First-Order Non-Linear Gravity
• Cosmological Evolution in 1/R-Gravity Theory
• Modified Friedmann Equations in R${}^{-1}$-Modified Gravity
• Holography of Gravitational Action Functionals
• Palatini Formulation of Modified Gravity with $\ln R$ Terms
• Cosmic Acceleration and Modified Gravitational Models
• Constraining Inverse Curvature Gravity with Supernovae
• f(R) theories of gravity in Palatini approach matched with observations
• Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
• Universality of Einstein Equations for the Ricci Squared Lagrangians
• Viscous FRW Cosmology in Modified Gravity
• Viable Palatini-f(R) cosmologies with generalized dark matter
• Generalized second law in modified theory of gravity
• Constraining dark energy models using the lookback time to galaxy clusters and the age of the universe
• Curvature driven acceleration : a utopia or a reality ?
• Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory
• Consistency of $f(R)=\sqrt{R^2-R_0^2}$ Gravity with the Cosmological Observations in Palatini Formalism
• Acceleration of the universe in the Einstein frame of a metric-affine f(R) gravity
• $R^2$ corrections to the cosmological dynamics of inflation in the Palatini formulation
• Cosmological perturbations in Palatini modified gravity
• Horizon Entropy in Modified Gravity
• Palatini approach to 1/R gravity and its implications to the late Universe
• Conformal entropy for generalised gravity theories as a consequence of horizon properties
• Universal field equations for metric-affine theories of gravity

Cited by in corpus (49)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Thermodynamics of cosmological horizons in $f(T)$ gravity
• On the stability of the cosmological solutions in f(R,G) gravity
• Palatini $f(R)$ Black Holes in Nonlinear Electrodynamics
• Black Hole Thermodynamics in MOdified Gravity (MOG)
• Dark energy, inflation and dark matter from modified F(R) gravity
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Instabilities and Anti-Evaporation of Reissner-Nordström Black Holes in modified $F(R)$ gravity
• Thermodynamics in $f(R)$ gravity in the Palatini formalism
• Black hole entropy in scalar-tensor and f(R) gravity: an overview
• Horizon thermodynamics in $f(R)$ theory
• Black hole entropy in modified gravity models
• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
• Making sense of the bizarre behaviour of horizons in the McVittie spacetime
• The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity
• Thermodynamic properties of modified gravity theories
• Are quantization rules for horizon areas universal?
• Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories
• An analysis of the Sultana-Dyer cosmological black hole solution of the Einstein equations
• R^n gravity and the chameleon
• The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions
• Effects of modified gravity on the turnaround radius in cosmology
• Modified entropies, their corresponding Newtonian forces, potentials, and temperatures
• Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity
• $f(R)$-Modified Gravity, Wald Entropy, and the Generalized Uncertainty Principle
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• Variational principle and boundary terms in gravity à la Palatini
• Lagrangian formulation of the Tsallis entropy
• Entanglement Entropy and Phase Portrait of f(R)-AdS Black Holes in the Grand Canonical Ensemble
• Black hole formation from a null fluid in extended Palatini gravity
• Dilaton Dark Energy Model in f(R), f(T) and Horava-Lifshitz Gravities
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Entropy and Energy of Static Spherically Symmetric Black Hole in $f(R)$ theory
• Calculating the Hawking Temperature of Black Holes in $f(Q)$ Gravity Using the RVB Method: A Residue-Based Approach
• Thermodynamics of black hole in $D$-dimensional $f(R)$ theory
• D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields
• Modified gravity from an entropy functional
• Thermodynamic Behavior of Time-Dependent Wormholes in Palatini $f(R)$ Gravity
• Study of Some Cosmological Parameters for Interacting New Holographic Dark Energy Model in f(T) Gravity
• The holographic bound in the scalar-tensor and $f(R)$ gravities
• Calculating the Hawking Temperatures of Kerr-Newman Black Holes in the f(R) Gravity Models with the RVB Method
• Revisiting Lifshitz-type solutions in $R^2$-corrected gravity
• Off-Shell ADT Conserved Quantities in Palatini Gravity