  We show in the context of Einstein gravity that the removal of a spatial
region leads to the appearance of an infinite set of observables and their
associated edge states localized at its boundary. Such a boundary occurs in
certain approaches to the physics of black holes like the one based on the
membrane paradigm. The edge states can contribute to black hole entropy in
these models. A ``complementarity principle" is also shown to emerge whereby
certain ``edge" observables are accessible only to certain observers. The
physical significance of edge observables and their states is discussed using
their similarities to the corresponding quantities in the quantum Hall effect.
The coupling of the edge states to the bulk gravitational field is demonstrated
in the context of (2+1) dimensional gravity.
