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

Journal Article · Thu Mar 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.064008· OSTI ID:21020154

Ronggen, Cai; Liming, Cao ^[1]

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1. Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080 (China)

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.

• OSTI ID: 21020154
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
COSMOLOGY
ENERGY-MOMENTUM TENSOR
ENTROPY
FIELD EQUATIONS
GENERAL RELATIVITY THEORY
GRAVITATION
SCALARS
THERMODYNAMICS
TRAPPING
UNIVERSE