Black holes in the conical ensemble

TL;DR

This paper investigates black holes with conical singularities in a finite cavity, analyzing their thermodynamics and contributions to the canonical ensemble, revealing that singular configurations influence the partition function but are not the ground state.

Contribution

It introduces the inclusion of conical singularities in the Euclidean path integral for black hole thermodynamics, extending the analysis to non-smooth solutions in a finite cavity setting.

Findings

Conical singularities increase free energy compared to smooth black holes.

Configurations with small deficit angles can have lower internal energy.

The ground state in the ensemble is never a singular black hole.

Abstract

We consider black holes in an "unsuitable box": a finite cavity coupled to a thermal reservoir at a temperature different than the black hole's Hawking temperature. These black holes are described by metrics that are continuous but not differentiable due to a conical singularity at the horizon. We include them in the Euclidean path integral sum over configurations, and analyze the effect this has on black hole thermodynamics in the canonical ensemble. Black holes with a small deficit (or surplus) angle may have a smaller internal energy or larger density of states than the nearby smooth black hole, but they always have a larger free energy. Furthermore, we find that the ground state of the ensemble never possesses a conical singularity. When the ground state is a black hole, the contributions to the canonical partition function from configurations with a conical singularity are comparable to the contributions from smooth fluctuations of the fields around the black hole background. Our focus is on highly symmetric black holes that can be treated as solutions of two-dimensional dilaton gravity models: examples include Schwarzschild, asymptotically Anti-de Sitter, and stringy black holes.