In a non-flat Friedmann universe, the unified first law dE = TdS + WdV and the energy-flux form -dE = TdS are consistent only when the horizon volume is taken as the areal volume, not the proper invariant volume.
Thermodynamics of Apparent Horizon in Brane World Scenario
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abstract
In this paper we discuss thermodynamics of apparent horizon of an $n$-dimensional Friedmann-Robertson-Walker (FRW) universe embedded in an $(n+1)$-dimensional AdS spacetime. By using the method of unified first law, we give the explicit entropy expression of the apparent horizon of the FRW universe. In the large horizon radius limit, this entropy reduces to the $n$-dimensional area formula, while in the small horizon radius limit, it obeys the $(n+1)$-dimensional area formula. We also discuss the corresponding bulk geometry and study the apparent horizon extended into the bulk. We calculate the entropy of this apparent horizon by using the area formula of the $(n+1)$-dimensional bulk. It turns out that both methods give the same result for the apparent horizon entropy. In addition, we show that the Friedmann equation on the brane can be rewritten to a form of the first law, $dE=TdS +WdV$, at the apparent horizon.
fields
gr-qc 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe
In a non-flat Friedmann universe, the unified first law dE = TdS + WdV and the energy-flux form -dE = TdS are consistent only when the horizon volume is taken as the areal volume, not the proper invariant volume.