Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

Abstract

There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity TdS = dE + PdV. We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons. In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.

arXiv commentrevtex; 6 pages; no figures

References in corpus (22)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Quantum gravity and minimum length
• The Thermodynamics of Black Holes
• Gravity and the Thermodynamics of Horizons
• Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
• Weaving a classical geometry with quantum threads
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Superfluid analogies of cosmological phenomena
• Entropy of Static Spacetimes and Microscopic Density of States
• Entropy of Null Surfaces and Dynamics of Spacetime
• Duality and zero-point length of spacetime
• Production and decay of evolving horizons
• Holography of Gravitational Action Functionals
• The Holography of Gravity encoded in a relation between Entropy, Horizon area and Action for gravity
• Holographic Gravity and the Surface term in the Einstein-Hilbert Action
• Dirty black holes: Symmetries at stationary non-static horizons
• Thermodynamics and/of Horizons: A Comparison of Schwarzschild,RINDLER and desitter Spacetimes
• Is gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence
• Quantum structure of spacetime and blackhole entropy
• Event horizon - Magnifying glass for Planck length physics
• Topological interpretation of the horizon temperature

Cited by in corpus (109)

• Thermodynamical Aspects of Gravity: New insights
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Friedmann Equations from Entropic Force
• Modified Friedmann Equations from Tsallis Entropy
• Horizon Thermodynamics and Gravitational Field Equations in Horava-Lifshitz Gravity
• Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Is gravitational entropy quantized ?
• Does the mass of a black hole decrease due to the accretion of phantom energy
• Generalized Misner-Sharp Energy in f(R) Gravity
• Thermodynamical interpretation of the geometrical variables associated with null surfaces
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• Emergent perspective of Gravity and Dark Energy
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Notes on Entropy Force in General Spherically Symmetric Spacetimes
• Black hole entropy in scalar-tensor and f(R) gravity: an overview
• Horizon thermodynamics in $f(R)$ theory
• Corrections to Hawking-like Radiation for a Friedmann-Robertson-Walker Universe
• Lanczos-Lovelock gravity from a thermodynamic perspective
• Charged Rotating BTZ Black Hole and Thermodynamic Behavior of Field Equations at its Horizon
• Hydrodynamics of spacetime and vacuum viscosity
• Conservative entropic forces
• Universality of P-V Criticality in Horizon Thermodynamics
• Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment
• Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity
• Generalized second law of thermodynamics in warped DGP braneworld
• Growth of Perturbations in Tsallis and Barrow Cosmology
• What is the fate of a black hole embedded in an expanding universe?
• Holography in Action
• The Hawking temperature of expanding cosmological black holes
• Response of Unruh-DeWitt detector with time-dependent acceleration
• Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions
• Distribution function of the Atoms of Spacetime and the Nature of Gravity
• Observational constraints of the modified cosmology through Barrow entropy
• Thermodynamics of Fractal Universe
• Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length
• Misner-Sharp Mass and the Unified First Law in Massive Gravity
• Tsallis cosmology and its applications in dark matter physics with focus on IceCube high-energy neutrino data
• Observational constraints on Tsallis modified gravity
• Gravity and Quantum Theory: Domains of Conflict and Contact
• The modified first laws of thermodynamics of anti-de Sitter and de Sitter space-times
• Thermodynamics of scalar-tensor theory with non-minimally derivative coupling
• Note on the emergence of cosmic space in modified gravities
• Accelerated Expansion of the Universe based on Emergence of Space and Thermodynamics of the Horizon
• Finite entanglement entropy from the zero-point-area of spacetime
• Emergence of spacetime dynamics in entropy corrected and braneworld models
• Criticality and Surface Tension in Rotating Horizon Thermodynamics
• An interacting New Holographic Dark Energy in the framework of fractal cosmology
• Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole
• Deformation of Codimension-2 Surface and Horizon Thermodynamics
• Horizon Thermodynamics from Einstein's Equation of State
• A note of the first law of thermodynamics by gravitational decoupling
• Noether Current, Black Hole Entropy and Spacetime Torsion
• Quasilocal energy in modified gravity
• Regular black holes with $\Lambda >0$ and its evolution in Lovelock gravity
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Inflation Based on the Tsallis Entropy
• Thermodynamics of Evolving Lorentzian Wormholes at Apparent Horizon in $f(R)$ Theory of Gravity
• Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories
• Quantum corrections to the entropy of charged rotating black holes
• Modified Friedmann equations from fractional entropy
• Thermodynamic of universe with a varying dark energy component
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force
• Apparent dark matter as a non-local manifestation of emergent gravity
• Investigation of generalised uncertainty principle effects on FRW cosmology
• Quantum Corrections for ABGB Black Hole
• A new class of regular black hole solutions with quasi-localized sources of matter in $(2+1)$ dimensions
• Local Approach to Hawking Radiation
• Bouncing universe from a modified dispersion relation
• Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons
• Is gravity entropic force?
• The thermal entropy density of spacetime
• Quantum corrections to the entropy of Einstein-Maxwell dilaton-axion black holes
• Covariant approach to the thermodynamic structure of a generic null surface
• Bouncing universe with modified dispersion relation
• Charged black holes in higher-dimensional Eddington-inspired Born-Infeld gravity
• Emergence of space and expansion of universe
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• On entropic gravity: the entropy postulate, entropy content of screens and relation to quantum mechanics
• Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling
• Thermodynamics of acoustic black holes in two dimensions
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Thermodynamics of Black String from Rényi entropy in de Rham-Gabadadze-Tolley Massive Gravity Theory
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• Thermodynamics of Graviton Condensate
• Entropy and Energy of Static Spherically Symmetric Black Hole in $f(R)$ theory
• Quasilocal mass in scalar-tensor gravity: spherical symmetry
• Horizon thermodynamics in fourth-order gravity
• Energy decomposition within Einstein-Born-Infeld black holes
• Exponential correction to Friedmann equations
• Spacetime mappings of the Brown-York quasilocal energy
• Entropy of cosmological black holes and generalized second law in phantom energy-dominated universe
• Thermodynamics of black hole in $D$-dimensional $f(R)$ theory
• Sakharov's induced gravity and the Poincaré gauge theory
• Friedmann equations from GUP-modified equipartition law
• Discussion of a possible corrected black hole entropy
• Thermodynamic structure of field equations near apparent horizon for radiating black holes
• Recovering semiclassical Einstein's equation using generalized entropy
• Gravity as a thermodynamic phenomenon
• The Smarr formula within the Geroch-Held-Penrose formalism
• A dynamical systems perspective on the thermodynamics of late-time cosmology
• Black holes and their horizons in semiclassical and modified theories of gravity
• Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory
• Modifying horizon thermodynamics by surface tensions
• Thermal nature of a generic null surface
• Penrose-Rindler equation and horizon thermodynamics of stationary black holes