Local conditions for the generalized covariant entropy bound

Abstract

A set of sufficient conditions for the generalized covariant entropy bound given by Strominger and Thompson is as follows: Suppose that the entropy of matter can be described by an entropy current $s^a$. Let $k^a$ be any null vector along $L$ and $s\equiv -k^a{s}_a$. Then the generalized bound can be derived from the following conditions: (i) $s^{\prime }\le 2\pi T_{ab}{k}^a{k}^b$, where $s'=k^a\grad_a s$ and $T_{ab}$ is the stress energy tensor; (ii) on the initial 2-surface $B$, $s(0)\le -1/4\theta (0)$, where $\theta$ is the expansion of $k^a$. We prove that condition (ii) alone can be used to divide a spacetime into two regions: The generalized entropy bound holds for all light sheets residing in the region where $s<-1/4\theta$ and fails for those in the region where $s>-1/4\theta$. We check the validity of these conditions in FRW flat universe and a scalar field spacetime. Some apparent violations of the entropy bounds in the two spacetimes are discussed. These holographic bounds are important in the formulation of the holographic principle.

10 pages, 7 figures

References in corpus (5)

• The holographic principle
• Simple sufficient conditions for the generalized covariant entropy bound
• A Quantum Bousso Bound
• The covariant entropy bound in gravitational collapse
• Probing entropy bounds with scalar field spacetimes

Cited by in corpus (1)

• Generalized Covariant Entropy Bound in Lanczos-Lovelock Gravity