A Note on Black Hole Entropy and Wormhole Instabilities

TL;DR

This paper examines how Euclidean wormholes influence black hole entropy calculations, identifies instabilities in saddle-point manifolds, and proposes a microcanonical approach to resolve related conceptual issues.

Contribution

It introduces a microcanonical formulation to handle instabilities in saddle points, improving the understanding of black hole entropy computations involving wormholes.

Findings

Instabilities in saddle-point manifolds can undermine Euclidean path integral interpretations.

A microcanonical approach effectively addresses these instabilities.

The method clarifies the role of wormholes in black hole entropy calculations.

Abstract

We discuss recent approaches to the computation of black hole entropies through semiclassical estimates of appropriate state overlaps, saturated by Euclidean wormhole configurations. We notice that the relevant saddle-point manifolds may exhibit instabilities, thereby compromising the interpretation of the Euclidean path integral as a tool for computing positive-definite inner products. We show that a proper treatment using a microcanonical formulation effectively addresses the puzzles posed by these instabilities.