The four laws of black hole mechanics

1973/06/01 by J. M. Bardeen, J. Bardeen, B. Carter +1 · 3,982 citations
Physics and Astronomy · #Analogy #Black Holes and Theoretical Physics #Black hole (networking) #Black hole thermodynamics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Entropy (arrow of time) #Event (particle physics) #Event horizon #Extremal black hole #Laws of thermodynamics #Mechanics #Membrane paradigm #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Rotational symmetry #Thermodynamics #White hole #de Sitter–Schwarzschild metric

paper · doi:10.1007/bf01645742

published in Communications in Mathematical Physics 31(2), 161-170 (Springer Science+Business Media)

openalex publication_date 1973/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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• Phase transition and Clapeyron equation of black holes in higher dimensional AdS spacetime
• Charge conservation, entropy current and gravitation
• The violation of the no-hair conjecture in four-dimensional ungauged supergravity
• Thermodynamics and phase transitions of nonlinear electrodynamics black holes in an extended phase space
• Equivalence of the modified gravity equation to the Clausius relation
• Universal thermodynamics in different gravity theories: Conditions for generalized second law of thermodynamics and thermodynamical equilibrium on the horizons
• Electromagnetic energy for a charged Kerr black hole in a uniform magnetic field
• Fermion tunneling beyond semiclassical approximation
• Constructing black hole entropy from gravitational collapse
• ΛCDM model inf(T) gravity: reconstruction, thermodynamics and stability
• Phase structures of the black Dp-D(p + 4)-brane system in various ensembles II: electrical and thermodynamic stability
• Observational constraints of the modified cosmology through Barrow entropy
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild anti-de Sitter black holes
• Extrinsic and intrinsic curvatures in thermodynamic geometry
• Spin and mass of the nearest supermassive black hole
• Entropy relations and bounds of horizons in modified gravity
• Thermodynamics of shearing massless scalar field spacetimes is inconsistent with the Weyl curvature hypothesis
• The first law and Wald entropy formula of heterotic stringy black holes at first order in α′
• Holographic Rényi Entropy at High Energy Density
• CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula
• Stable remnants and quantum gravity effects in nonlinear electric source Culetu black hole
• New insights into thermodynamics and microstructure of AdS black holes
• Modified Newtonian Dynamics as an Entropic Force
• On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry
• Thermodynamics of black hole horizons and Kerr/CFT correspondence
• Thermodynamics of d-dimensional charged AdS (Anti-de sitter) black holes: Hamiltonian approach and Clapeyron equation
• Boulware state and the generalized second law of thermodynamics
• Area law unification and the holographic event horizon
• Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble
• ESSENTIAL AND INESSENTIAL FEATURES OF HAWKING RADIATION
• Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics
• The Fundamental Equilibrium Equation For Gaseous Stars And The\n Tolman-Oppenheimer-Volkoff Equation -- Derivations And Applications With\n Emphasis On Optimisational-Variational Methods
• A gravitational entropy proposal
• Silhouettes of invisible black holes
• Horizon entropy and higher curvature equations of state
• Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling
• A new phenomenological definition of entropy and application to black\n holes
• Logarithmic correction to the entropy of extremal black holes in N = 1 Einstein-Maxwell supergravity
• Joule-Thomson expansion of Reissner-Nordström-Anti-de Sitter black holes with cloud of strings and quintessence
• Spacetime Causal Structure and Dimension from Horismotic Relation
• Thermodynamics of the inhomogeneous perfect fluid LTB model: modified Bekenstein–Hawking system
• Brick walls on the brane
• Euclidean Thermodynamics and Lyapunov Exponents of Einstein-Power-Yang-Mills AdS Black Holes
• Static vacuum solutions in non-Riemannian gravity
• Barrow and Tsallis entropies after the DESI DR2 BAO data
• Area spectrum and black hole thermodynamics
• Isolated and Dynamical Horizons and Their Applications
• Can shadows connect black hole microstructures?
• Information--Theoretic Black Hole Entropy II: Infrared Gravity and Charged/Rotating Extensions
• Information-Theoretic Black Hole Entropy I: Beyond the Area Law
• Mechanics of isolated horizons
• Astrophysical black hole horizons in a cosmological context: Nature and possible consequences on Hawking radiation
• Higher-Derivative Corrections to Reissner--Nordström Black Holes from Worldline QFT
• Gravitational entropy in black hole transformations
• Probing Black Hole Phase Transitions through Quasi-Periodic Oscillations
• Staticity theorem for a higher dimensional generalized Einstein-Maxwell system
• Asymptotic symmetries on the Kerr–Newman horizon without the anomaly of diffeomorphism invariance
• Energy Conservation for Dynamical Black Holes
• Quantum-bias cosmology: Acceleration from holographic information capacity
• Tunnelling methods and Hawking's radiation: achievements and prospects
• First law of binary black hole mechanics in general relativity and post-Newtonian theory
• Holographic cosmology from the first law of thermodynamics and the generalized uncertainty principle
• Scattering of fermions off dilaton black holes
• Source vacuum fluctuations of black-hole radiance
• Lower-dimensional black hole chemistry
• The canonical ensemble of a self-gravitating matter thin shell in AdS
• The first law of soliton and black hole mechanics in five dimensions
• Thermodynamic supercriticality and complex phase diagram for the AdS black hole
• Thermodynamic properties of Kehagias-Sfetsos black hole and KS/CFT correspondence
• Violation of the third law of black hole mechanics in vacuum gravity
• General relativity [wikipedia]
• Classification of Near-Horizon Geometries of Extremal Black Holes. [europepmc]
• The Thermodynamics of Black Holes. [europepmc]
• Isolated and Dynamical Horizons and Their Applications. [europepmc]
• Quasi-Local Energy-Momentum and Angular Momentum in General Relativity. [europepmc]
• f ( R ) Theories. [europepmc]
• Analogue Gravity. [europepmc]
• Stationary Black Holes: Uniqueness and Beyond. [europepmc]
• The Kerr/CFT Correspondence and its Extensions. [europepmc]
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries. [europepmc]
• Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article. [europepmc]
• Analogue Gravity. [europepmc]
• The Kerr/CFT correspondence and its extensions. [europepmc]
• Stationary Black Holes: Uniqueness and Beyond. [europepmc]
• Surfaces away from horizons are not thermodynamic. [europepmc]
• What Constitutes Emergent Quantum Reality? A Complex System Exploration from Entropic Gravity and the Universal Constants. [europepmc]
• Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity. [europepmc]
• A Note on the Entropy Force in Kinetic Theory and Black Holes. [europepmc]
• Comment on "Black Hole Entropy: A Closer Look". [europepmc]
• What Is Heat? Can Heat Capacities Be Negative? [europepmc]
• Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles. [europepmc]
• The Quantum Memory Matrix: A Unified Framework for the Black Hole Information Paradox. [europepmc]
• Thermodynamics of Observations. [europepmc]
• Matrix Quantum Mechanics and Entanglement Entropy: A Review. [europepmc]
• Minimum Spacetime Length and the Thermodynamics of Spacetime. [europepmc]
• Toward a Tripartite Taxonomy of Entropy in Physics [europepmc]