Thermodynamical interpretation of the geometrical variables associated with null surfaces

Abstract

The emergent gravity paradigm interprets gravitational field equations as describing the thermodynamic limit of the underlying statistical mechanics of microscopic degrees of freedom of the spacetime. The connection is established by attributing a heat density Ts to the null surfaces where T is the appropriate Davies-Unruh temperature and s is the entropy density. The field equations can be obtained from a thermodynamic variational principle which extremizes the total heat density of all null surfaces. The explicit form of s determines the nature of the theory. We explore the consequences of this paradigm for an arbitrary null surface and highlight the thermodynamic significance of various geometrical quantities. In particular, we show that: (a) A conserved current, associated with the time development vector in a natural fashion, has direct thermodynamic interpretation in all Lanczos-Lovelock models of gravity. (b) One can generalize the notion of gravitational momentum, introduced in arXiv 1506.03814 to all Lanczos-Lovelock models of gravity such that the conservation of the total momentum leads to the relevant field equations. (c) The thermodynamic variational principle which leads to the field equations of gravity can also be expressed in terms of the gravitational momentum in all Lanczos-Lovelock models. (d) Three different projections of gravitational momentum related to an arbitrary null surface in the spacetime lead to three different equations, all of which have thermodynamic interpretation. The first one reduces to a Navier-Stokes equation for the transverse drift velocity. The second can be written as a thermodynamic identity TdS = dE + P dV. The third describes the time evolution of the null surface in terms of suitably defined surface and bulk degrees of freedom. The implications are discussed.

v2, Published version

References in corpus (15)

• 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
• Dark Energy and Gravity
• Entropy of Null Surfaces and Dynamics of Spacetime
• Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Emergent Gravity Paradigm: Recent Progress
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Lanczos-Lovelock gravity from a thermodynamic perspective
• Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity
• Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity
• Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity
• The thermodynamic structure of Einstein tensor
• Momentum density of spacetime and the gravitational dynamics

Cited by in corpus (71)

• Cosmological model from the holographic equipartition law with a modified Rényi entropy
• Photon orbits and thermodynamic phase transition of $d$-dimensional charged AdS black holes
• Solving higher curvature gravity theories
• Universality of P-V Criticality in Horizon Thermodynamics
• Black Holes: Eliminating Information or Illuminating New Physics?
• Emergent cosmic space in Rastall theory
• Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet Gravity
• Boundary terms of the Einstein-Hilbert action
• Buchdahl compactness limit for a pure Lovelock static fluid star
• Probing Phase Structure of Black Holes with Lyapunov Exponents
• Probing the relationship between the null geodesics and thermodynamic phase transition for rotating Kerr-AdS black holes
• Distribution function of the Atoms of Spacetime and the Nature of Gravity
• Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy
• Generalized thermodynamic constraints on holographic-principle-based cosmological scenarios
• Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble
• Gravity and Quantum Theory: Domains of Conflict and Contact
• Brown-York quasilocal energy in Lanczos-Lovelock gravity and black hole horizons
• Photon sphere and reentrant phase transition of charged Born-Infeld-AdS black holes
• 1/r potential in higher dimensions
• Criticality and Surface Tension in Rotating Horizon Thermodynamics
• Action growth for black holes in modified gravity
• Raychaudhuri equation with zero point length
• Thermodynamics of two black holes
• Universal thermodynamic topological classes of static black holes in Conformal Killing Gravity
• Horizon Thermodynamics from Einstein's Equation of State
• Noether Current, Black Hole Entropy and Spacetime Torsion
• Entropy of a generic null surface from its associated Virasoro algebra
• Null boundary terms for Lanczos-Lovelock gravity
• Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source
• On the physical process first law for dynamical black holes
• Triple points and novel phase transitions of dyonic AdS black holes with quasitopological electromagnetism
• Exploring the Nature of Gravity
• Entropy of a box of gas in an external gravitational field $-$ revisited
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Photon sphere and phase transition of $d$-dimensional ($d\ge 5$) charged Gauss-Bonnet AdS black holes
• Horizon thermodynamics in holographic cosmological models with a power-law term
• Evolution of thermodynamic quantities on cosmological horizon in $\Lambda (t)$ model
• Discrete quantum spectrum of black holes
• Weiss variation for general boundaries
• Kinematics of Radion field: A possible source of dark matter
• Boundary Term in the Gravitational Action is the Heat Content of the Null surfaces
• Energy stored on a cosmological horizon and its thermodynamic fluctuations in holographic equipartition law
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Emergent Cosmos in Einstein-Cartan Theory
• Covariant approach to the thermodynamic structure of a generic null surface
• Entropy production due to adiabatic particle creation in a holographic dissipative cosmology
• Emergence of space and expansion of universe
• Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant
• Evolution of dissipative and non-dissipative universes in holographic cosmological models with a power-law term
• Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law
• Minimum-length Ricci scalar for null separated events
• Entropy and Gravitation: From Black Hole Computers to Dark Energy and Dark Matter
• Cosmological model based on both holographic-like connection and Padmanabhan's holographic equipartition law
• Information content and minimum-length metric: A drop of light
• Static Spherically Symmetric solutions in a subclass of Horndeski theories of gravity
• Comments on the entropic gravity proposal
• Holographic equipartition from first order action
• Geometrothermodynamics for Black holes and de Sitter Space
• Field equations for Lovelock gravity: An alternative route
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
• Kiselev black strings: the charged rotating solutions
• Perturbations of the almost Killing equation and their implications
• Lightlike singular hypersurfaces in quadratic gravity
• Embedding into flat spacetime and black hole thermodynamics
• General Relativity in Post Independence India
• Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model
• Modifying horizon thermodynamics by surface tensions
• Thermal nature of a generic null surface
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes
• Singularity avoidance from path integral