Edge states in Gravity and Black Hole Physics

TL;DR

This paper shows that removing a spatial region in gravity introduces an infinite set of boundary-localized edge observables, with a complementarity between observers determining which are accessible. It develops a canonical framework where edge observables arise from boundary terms and demonstrates, via a QHE analogy, how bulk-edge coupling is required for gauge invariance. The authors explicitly realize edge-bulk coupling in (2+1) gravity and argue that similar edge dynamics should exist in (3+1) gravity, suggesting a possible path to understanding black hole entropy and information retention through boundary degrees of freedom.

Abstract

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.