Thermodynamics of Apparent Horizon in Brane World Scenario

Details Thermodynamics of Apparent Horizon in Brane World Scenario Thermodynamics of Apparent Horizon in Brane World Scenario

2006-12-14

arxiv.org/abs/hep-th/0612144v3

Nucl.Phys.B785:135-148,2007

Physics

High Energy Physics

High Energy Physics - Theory

latex, 16 pages with one figure, V2: two references added; V3: to appear in Nucl. Phys. B

Scientific paper

10.1016/j.nuclphysb.2007.06.016

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.

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