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

By R. Cai, Li-Ming Cao. 2006

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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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec04172058c160dda8071b6a19c4820018f2099b

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Citations in the corpus

f(R) Theories (2010, background): “33) Following [297, 298, 108] we introduce the work density W = (ρd + ρM − Pd − PM )/2.”
Black hole chemistry: thermodynamics with Lambda (2016, positive): “After Hawking’s seminal paper [4] elevated the laws of black hole mechanics to the laws of thermodynamics, identifying the geometric concept of surface gravity κ with the quantum mechanical temperature of the black hole, κ ∝ T ħ , two important questions arose: How do the completely classical Einste”