The self-gravitational corrections as the source for stiff matter on the brane in [formula omitted] bulk

Abstract

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.