Black hole entropy and Lorentz-diffeomorphism Noether charge

Abstract

We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.

8 pages, double-column; This version: references updated; added another example in section III. This version matches the published version

References in corpus (4)

• Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry
• Surface terms, Asymptotics and Thermodynamics of the Holst Action
• Gravity as a constrained BF theory: Noether charges and Immirzi parameter
• General theory of Lie derivatives for Lorentz tensors

Cited by in corpus (74)

• Edge modes of gravity -- I: Corner potentials and charges
• Local phase space and edge modes for diffeomorphism-invariant theories
• The Weyl BMS group and Einstein's equations
• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• Lorentz-diffeomorphism edge modes in 3d gravity
• A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
• Boundary effects in General Relativity with tetrad variables
• BMS current algebra in the context of the Newman-Penrose formalism
• A gauge-invariant symplectic potential for tetrad general relativity
• Holographic spin liquids and Lovelock Chern-Simons gravity
• Black hole scalar charge from a topological horizon integral in Einstein-dilaton-Gauss-Bonnet gravity
• Asymptotic gravitational charges
• The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime
• Hamiltonian derivation of dual gravitational charges
• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
• Noether charge and black hole entropy in teleparallel gravity
• Static and rotating black strings in dynamical Chern-Simons modified gravity
• A note on dual gravitational charges
• T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$
• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity
• Conserved Charges in Extended Theories of Gravity
• The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime
• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Magnetic charges and Wald entropy
• Black hole entropy in the Chern-Simons-like theories of gravity and Lorentz-diffeomorphism Noether charge
• Black hole chemistry, the cosmological constant and the embedding tensor
• T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm
• Luminal Propagation of Gravitational Waves in Scalar-tensor Theories: The Case for Torsion
• Surface Charges for Gravity and Electromagnetism in the First Order Formalism
• Entropy in Poincaré gauge theory: Hamiltonian approach
• Hair loss in parity violating gravity
• Komar integral and Smarr formula for axion-dilaton black holes versus S duality
• T-duality equivalences beyond string theory
• Covariant phase space for gravity with boundaries: metric vs tetrad formulations
• Gravitational memory effects and higher derivative actions
• Lorentz-diffeomorphism Conserved Charges And Virasoro Algebra In Chern-Simons-Like Theories Of Gravity
• Entropy of Reissner-Nordström-like black holes
• Enhanced asymptotic $BM{S}_3$ algebra of the flat spacetime solutions of generalized minimal massive gravity
• First law of black hole mechanics with fermions
• Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity
• Entropy in Poincaré gauge theory: Kerr-AdS solution
• Near horizon gravitational charges
• General formulas for conserved charges and black hole entropy in Chern-Simons-like theories of gravity
• Emergent Cosmos in Einstein-Cartan Theory
• Higher derivative asymptotic charges and internal Lorentz symmetries
• Gauge Invariant Derivation of Zeroth and First Laws of Black Hole Thermodynamics
• Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
• On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries
• Thermodynamics of Riemannian Kerr-AdS black holes in Poincaré gauge theory
• Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
• Conserved currents in the Palatini formulation of general relativity
• Quasi-local conserved charges in Lorentz-diffeomorphism covariant theory of gravity
• First law of black hole mechanics in variable background fields
• Warped $Ad{S}_3$ black hole in minimal massive gravity with first order formalism
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization
• Null boundary gravitational charges from local Lorentz symmetries
• Geometrothermodynamics for Black holes and de Sitter Space
• Quasilocal first law of black hole dynamics from local Lorentz transformations
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• Linear Newman-Penrose charges as subleading BMS and dual BMS charges
• Off-shell Noether currents and potentials for first-order general relativity
• Quasi-Local Conserved Charges of Spin-3 Topologically Massive Gravity
• Mass and angular momentum of black holes in 3D gravity theories with first order formalism
• Quasi-local Energy in 3D Gravity with Torsion
• Perturbations of the almost Killing equation and their implications
• First Law of Black Hole in the Gravitational Electromagnetic System
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory
• Mechanics of Isolated Horizons in Scalar-Tensor Theories
• On the unexpected geometrical origin of the algebra of symmetries