A Note on Black Hole Entropy and Wormhole Instabilities

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.