Brane-Bulk Interaction and Holographic Principle

Abstract

We introduce the brane-bulk interaction to discuss a limitation of the cosmological Cardy-Verlinde formula which is useful for the holographic description of brane cosmology. In the presence of the brane-bulk interaction, we cannot find the entropy representation of the first Friedmann equation (the cosmological Cardy-Verlinde formula). In the absence of the interaction, the cosmological Cardy-Verlinde formula is established even for the time-dependent charged AdS background. Hence, if there exists a dynamic exchange of energy between the brane and the bulk (that is, if ${\tilde{T}}^t{}_y\ne 0$), we cannot achieve the cosmological holographic principle on the brane.

9 pages, REVTEX