Black hole wavefunctions and microcanonical states

TL;DR

This paper constructs a microcanonical thermofield double state for black holes using gravitational path integrals, analyzing its properties and overlaps with canonical states in a semiclassical framework.

Contribution

It introduces a method to define microcanonical black hole states via boundary conditions and computes their overlaps with canonical states semiclassically.

Findings

Derived a semiclassical approximation for microcanonical states

Calculated overlaps with canonical thermofield double states

Identified saddlepoint geometries as higher-dimensional wedges

Abstract

We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the Hartle-Hawking wavefunction of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity.