Unified first law and the thermodynamics of the apparent horizon in the FRW universe

2006/11/30 by Rong-Gen Cai, Li-Ming Cao · 20 citations
Physics and Astronomy · #Apparent horizon #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Event horizon #First law of thermodynamics #Friedmann–Lemaître–Robertson–Walker metric #Gravitation #Horizon #Mathematical physics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Second law of thermodynamics #Thermodynamics #Universe #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.75.064008

published as Phys.Rev.D75:064008,2007 · v2: revtex, 23 pages, references added, minor changes, to appear in PRD

arxiv created 2007/02/24 · openalex publication_date 2007/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we revisit the relation between the Friedmann equations and the first law of thermodynamics. We find that the unified first law first proposed by Hayward to treat the outertrapping horizon of a dynamical black hole can be used to the apparent horizon (a kind of inner trapping horizon in the context of the FRW cosmology) of the FRW universe. We discuss three kinds of gravity theorties: Einstein theory, Lovelock thoery, and scalar-tensor theory. In Einstein theory, the first law of thermodynamics is always satisfied on the apparent horizon. In Lovelock theory, treating the higher derivative terms as an effective energy-momentum tensor, we find that this method can give the same entropy formula for the apparent horizon as that of black hole horizon. This implies that the Clausius relation holds for the Lovelock theory. In scalar-tensor gravity, we find, by using the same procedure, the Clausius relation no longer holds. This indicates that the apparent horizon of the FRW universe in the scalar-tensor gravity corresponds to a system of nonequilibrium thermodynamics. We show this point by using the method developed recently by Eling et al. for dealing with the f(R) gravity.

Citations

• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Positivity of Quasilocal Mass
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• The four laws of black hole mechanics
• Thermodynamics of Spacetime: The Einstein Equation of State
• Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article
• Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse
• Particle creation by black holes
• Republication of: The dynamics of general relativity
• Black Holes and Entropy

Cited by

• The Rényi entropy and entropic cosmology
• THERMODYNAMICAL DESCRIPTION OF THE INTERACTING NEW AGEGRAPHIC DARK ENERGY
• Universality of P − V criticality in horizon thermodynamics
• Friedmann Equations and Thermodynamics of Apparent Horizons
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Generalized Vaidya spacetime in Lovelock gravity and thermodynamics on the apparent horizon
• Thermodynamics of interacting holographic dark energy with the apparent horizon as an IR cutoff
• Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy
• Thermodynamics of FRW universe with Chaplygin gas models
• Thermodynamics of scale-dependent Friedmann equations
• Misner-Sharp mass and the unified first law in massive gravity
• Quasilocal mass in scalar–tensor gravity: spherical symmetry
• Emergent dark matter in late time universe on holographic screen
• Thermodynamic analysis of modified teleparallel gravity involving higher-order torsion derivative terms
• Universal thermodynamics in different gravity theories: Conditions for generalized second law of thermodynamics and thermodynamical equilibrium on the horizons
• A study of Universal thermodynamics in Lanczos–Lovelock gravity
• Thermodynamical description of the ghost dark energy model
• Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling
• Probing interaction and spatial curvature in the holographic dark energy model
• Tunnelling methods and Hawking's radiation: achievements and prospects