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SELF-GRAVITATIONAL CORRECTIONS TO THE CARDY–VERLINDE FORMULA AND THE FRW BRANE COSMOLOGY IN SdS₅ BULK

Physics Dept., Inst. for Studies in Theo. Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran, Iran

and

Departament d'Estructura i Constituents de la Matèria and CER for Astrophysics, Particle Physics and Cosmology, Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Spain

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https://doi.org/10.1142/S0217751X05023888Cited by:58 (Source: Crossref)

Abstract

The semiclassical corrections to the Cardy–Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole (SdS₅) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS₅ bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS₅ bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in such a way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the four-dimensional brane is presented.

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