Casimir Effect of Graviton and the Entropy Bound

TL;DR

This paper calculates the Casimir effect of thermal gravitons in an Einstein universe and discusses its implications for Verlinde's entropy bound and black p-brane thermodynamics.

Contribution

It demonstrates the necessity of including the graviton's Casimir effect to uphold Verlinde's entropy bound in weakly coupled CFTs.

Findings

Graviton Casimir effect prevents violation of Verlinde's bound.

Implications for thermodynamics of black p-branes.

Supports the higher-dimensional Cardy's formula in gravitational contexts.

Abstract

In this note we calculate the Casimir effect of free thermal gravitons in Einstein universe and discuss how it changes the entropy bound condition proposed recently by Verlinde [hep-th/0008140] as a higher dimensional generalization of Cardy's formula for conformal field theories (CFT). We find that the graviton's Casimir effect is necessary in order not to violate Verlinde's bound for weakly coupled CFT. We also comment on the implication of this new Cardy's formula to the thermodynamics of black $p$-brane.