Black Hole Entropy in Two Dimensions

TL;DR

This paper investigates black hole entropy in a two-dimensional gravity model using Noether charge techniques, demonstrating an entropy increase theorem and expressing entropy as a local horizon quantity.

Contribution

It extends Noether charge methods to non-local effective actions in 2D gravity, providing a local expression for black hole entropy and proving an increase theorem.

Findings

Entropy expressed as a local horizon quantity

Entropy satisfies an increase theorem

Method extended to non-local actions

Abstract

Black hole entropy is studied for an exactly solvable model of two-dimensional gravity\cite{rst1}, using recently developed Noether charge techniques\cite{wald1}. This latter approach is extended to accomodate the non-local form of the semiclassical effective action. In the two-dimensional model, the final black hole entropy can be expressed as a local quantity evaluated on the horizon. This entropy is shown to satisfy an increase theorem on either the global or apparent horizon of a two-dimensional black hole.