  We aim to establish the holographic principle as a universal law, rather than
a property only of static systems and special space-times. Our covariant
formalism yields an upper bound on entropy which applies to both open and
closed surfaces, independently of shape or location. It reduces to the
Bekenstein bound whenever the latter is expected to hold, but complements it
with novel bounds when gravity dominates. In particular, it remains valid in
closed FRW cosmologies and in the interior of black holes. We give an explicit
construction for obtaining holographic screens in arbitrary space-times (which
need not have a boundary). This may aid the search for non-perturbative
definitions of quantum gravity in space-times other than AdS.
