Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe

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dc.creatorCai, Rong-Gen
dc.creatorCao, Li-Ming
dc.date2006-11-14
dc.date2007-02-24
dc.date.accessioned2026-07-07T10:41:07Z
dc.date.available2026-07-07T10:41:07Z
dc.descriptionIn this paper we revisit the relation between the Friedmann equations and the first law of thermodynamics. We find that the unified first law firstly proposed by Hayward to treat the "outer"trapping horizon of 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 FRW universe in the scalar-tensor gravity corresponds to a system of non-equilibrium thermodynamics. We show this point by using the method developed recently by Eling {\it et al.} for dealing with the $f(R)$ gravity.
dc.descriptionv2: revtex, 23 pages, references added, minor changes, to appear in PRD
dc.identifierhttps://arxiv.org/abs/gr-qc/0611071
dc.identifierhttp://arxiv.org/abs/gr-qc/0611071
dc.identifierPhys.Rev.D75:064008,2007
dc.identifierdoi:10.1103/PhysRevD.75.064008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/181530
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleUnified First Law and Thermodynamics of Apparent Horizon in FRW Universe
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