A Causal Entropy Bound

TL;DR

This paper introduces a new covariant entropy bound called the causal entropy bound, which interpolates between Bekenstein's and holographic bounds depending on gravitational strength, and is validated in various scenarios.

Contribution

It proposes a novel covariant entropy bound based on causal-connection scales, bridging existing bounds and analyzing their validity across different gravitational regimes.

Findings

The causal entropy bound scales as the square root of EV.

In limited gravity, Bekenstein's bound is the strongest.

In strong gravity, the new bound and Bousso's holographic bound outperform Bekenstein's.

Abstract

The identification of a causal-connection scale motivates us to propose a new covariant bound on entropy within a generic space-like region. This "causal entropy bound", scaling as the square root of EV, and thus lying around the geometric mean of Bekenstein's S/ER and holographic S/A bounds, is checked in various "critical" situations. In the case of limited gravity, Bekenstein's bound is the strongest while naive holography is the weakest. In the case of strong gravity, our bound and Bousso's holographic bound are stronger than Bekenstein's, while naive holography is too tight, and hence typically wrong.