ar X iv : h ep - t h / 05 02 10 9 v 1 1 1 Fe b 20 05 The Self - Gravitational Corrections as the Source for Stiff Matter on the Brane in SAdS 5 Bulk

A D3− brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. Taking into account the semi-classical corrections to the black hole entropy that arise as a result of the self-gravitational effect, and employing the AdS/CFT correspondence, we obtain the self-gravitational correction to the first Friedmann-like equation. The additional term in the Hubble equation due to the self-gravitational effect goes as a −6. Thus, the self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role.