Edge states in Gravity and Black Hole Physics

TL;DR

This paper investigates how removing a spatial region in Einstein gravity introduces boundary-localized edge states that contribute to black hole entropy, with implications for black hole physics and quantum gravity.

Contribution

It demonstrates the emergence of edge states at boundaries in Einstein gravity and explores their role in black hole entropy and observer-dependent observables.

Findings

Edge states appear at boundaries when regions are removed in Einstein gravity.

Edge states can contribute to black hole entropy.

Coupling of edge states to gravity shown in (2+1) dimensions.

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.