Causal entropy bound for a spacelike region

The identification of a causal-connection scale motivates us to propose a n ew covariant bound on entropy within a generic spacelike region; This "caus al entropy bound," scaling as root EV, and;thus lying around the geometric mean of Bekenstein's S/ER and holographic SIA 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 stro ng gravity, our bound and Bousso's holographic bound are stronger than Beke nstein's, while naive holography is too tight, and hence typically wrong.