EDGE STATES IN GRAVITY AND BLACK-HOLE PHYSICS

We show in the context of canonical gravity that the removal of a spat ial region leads to the appearance of an infinite set of observables a nd their associated edge states localized at its boundary. Such a boun dary occurs in certain approaches to the physics of black holes like t he one based on the membrane paradigm. The edge states can contribute to the black hole entropy in these models. A ''complementarity princip le'' is also shown to emerge whereby certain ''edge'' observables are accessible only to certain observers. The physical significance of edg e observables and their states are discussed using their similarities to the corresponding quantities in the quantum Hall effect, The coupli ng of the edge to the bulk states of the gravitational field is demons trated in the context of (2+1)-dimensional gravity.