Brane-Bulk Interaction and Holographic Principle

TL;DR

This paper investigates how brane-bulk interactions affect the holographic description of brane cosmology, revealing limitations in the applicability of the Cardy-Verlinde entropy formula when energy exchange occurs.

Contribution

It demonstrates that brane-bulk interactions prevent the derivation of the entropy form of the Friedmann equation, highlighting a key limitation in holographic brane cosmology models.

Findings

Brane-bulk interaction disrupts the entropy representation of the Friedmann equation.

Without interaction, the Cardy-Verlinde formula holds even in charged AdS backgrounds.

Energy exchange between brane and bulk inhibits the realization of the 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 $\tilde T^t~_y \not=0$), we cannot achieve the cosmological holographic principle on the brane.