English

Thermodynamics of Apparent Horizon in Brane World Scenario

High Energy Physics - Theory 2008-11-26 v3 General Relativity and Quantum Cosmology

Abstract

In this paper we discuss thermodynamics of apparent horizon of an nn-dimensional Friedmann-Robertson-Walker (FRW) universe embedded in an (n+1)(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 nn-dimensional area formula, while in the small horizon radius limit, it obeys the (n+1)(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)(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+WdVdE=TdS +WdV, at the apparent horizon.

Keywords

Cite

@article{arxiv.hep-th/0612144,
  title  = {Thermodynamics of Apparent Horizon in Brane World Scenario},
  author = {Rong-Gen Cai and Li-Ming Cao},
  journal= {arXiv preprint arXiv:hep-th/0612144},
  year   = {2008}
}

Comments

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