A Second Law for Higher Curvature Gravity

Abstract

The Second Law of black hole thermodynamics is shown to hold for arbitrarily complicated theories of higher curvature gravity, so long as we allow only linearized perturbations to stationary black holes. Some ambiguities in Wald's Noether charge method are resolved. The increasing quantity turns out to be the same as the holographic entanglement entropy calculated by Dong. It is suggested that only the linearization of the higher-curvature Second Law is important, when consistently truncating a UV-complete quantum gravity theory.

10 pages. Honorable mention 2015 Gravity Research Foundation Essay; Appendix A, footnotes, some citations, and minor textual changes added later. v2 corrected typo in Eq. (14) for the linearized Dong entropy. To appear in IJMPD

References in corpus (5)

• Entanglement entropy, conformal invariance and extrinsic geometry
• Topological deformation of isolated horizons
• On entanglement entropy functionals in higher derivative gravity theories
• The holographic entropy increases in quadratic curvature gravity
• A note on the resolution of the entropy discrepancy

Cited by in corpus (69)

• A Quantum Focussing Conjecture
• Deriving covariant holographic entanglement
• The Black Hole information problem: past, present, and future
• Covariant phase space with boundaries
• Local phase space and edge modes for diffeomorphism-invariant theories
• Aspects of general higher-order gravities
• Generalized entropy for general subregions in quantum gravity
• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Entanglement equilibrium for higher order gravity
• The holographic entropy increases in quadratic curvature gravity
• Pole skipping in holographic theories with bosonic fields
• f(Lovelock) theories of gravity
• The second law of black hole mechanics in effective field theory
• Black Hole Thermodynamics: General Relativity and Beyond
• Higher Curvature Gravity from Entanglement in Conformal Field Theories
• Microcanonical Action and the Entropy of Hawking Radiation
• An entropy current for dynamical black holes in four-derivative theories of gravity
• Entropy functionals and c-theorems from the second law
• Towards a second law for Lovelock theories
• Pole skipping in holographic theories with gauge and fermionic fields
• A Survey of Black Hole Thermodynamics
• The Quantum Null Energy Condition in Curved Space
• The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
• Holographic entanglement entropy for perturbative higher-curvature gravities
• Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law
• Dynamical Black Hole Entropy in Effective Field Theory
• A stationary black hole must be axisymmetric in effective field theory
• Holographic Entanglement for Chern-Simons Terms
• Area deficits and the Bel-Robinson tensor
• A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
• Non-extremal, ${\alpha }^{\prime }$-corrected black holes in 5-dimensional Heterotic Superstring Theory
• Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in $d\ge 5$ dimensions
• Reparametrization Symmetry of Local Entropy Production on a Dynamical Horizon
• Emergent Gravity in a Holographic Universe
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
• Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields
• Constraining the topological Gauss-Bonnet coupling from GW150914
• Non-vanishing of tidal Love numbers
• Generalized Gravitational Entropy from Total Derivative Action
• Investigating the Linearized Second Law in Horndeski Gravity
• Entropy Current and Fluid-Gravity Duality in Gauss-Bonnet theory
• Dynamical black hole entropy beyond general relativity from the Einstein frame
• Dynamical entropy of charged black objects
• Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality
• A holographic proof of the universality of corner entanglement for CFTs
• Entropy-current for dynamical black holes in Chern-Simons theories of gravity
• RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity
• Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity
• From spacetime thermodynamics to Weyl transverse gravity
• Higher-Curvature Gravity, Black Holes and Holography
• Generalized Vaidya spacetime for cubic gravity
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Apparent Horizons Associated with Dynamical Black Hole Entropy
• Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity
• Entropy increases at linear order in scalar-hairy Lovelock gravity
• Extremality as a Consistency Condition on Subregion Duality
• Entanglement Entropy and Thermodynamics of Dynamical Black Holes
• Thermalization and non-monotonic entanglement growth in an exactly solvable model
• Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D
• Generalized Second Law for Non-minimally Coupled Matter Theories
• Linearization (in)stabilities and crossed products
• Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory
• The linearized second law for any higher curvature gravity with the scalar and the electromagnetic fields
• The First Law of Black Hole Mechanics
• Higher-spin localized shocks
• An entropy current and the second law in higher derivative theories of gravity
• Black hole thermodynamics probes the equivalence principle
• Holographic Entanglement Entropy for Brane-World Higher Derivative Gravity