Holographic Weyl entropy bounds

We consider the entropy bounds recently conjectured by Fischler, Susskind, and Bousso, and proven in certain cases by Flanagan, Marolf, and Wald (FMW). One of the FMW derivations supposes a covariant form of the Bekenstein entropy bound, the consequences of which we explore. The derivation also suggests that the entropy contained in a vacuum spacetime, e.g., Schwarzschild spacetime, may be related to the shear on congruences of null rays. We find evidence for this intuition, but in a surprising way. We compare the covariant entropy bound to certain earlier discussions of black hole entropy, and comment on the separate roles of quantum mechanics and gravity in the entropy bound.