A Causal Entropy Bound

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.