Distorted vacuum black holes in the canonical ensemble

TL;DR

This paper investigates vacuum black holes within a finite cavity, revealing conditions for their existence, thermodynamic behavior, and the exclusion of certain horizonless spacetimes, using Israel's coordinate system.

Contribution

It demonstrates that only black holes or flat spacetime are possible inside a cavity without symmetry assumptions, and analyzes their thermodynamic properties.

Findings

Black holes or flat spacetime are the only possible static solutions inside a cavity.

Hawking temperature diverges as the horizon area shrinks.

Black hole phase dominates at high temperatures.

Abstract

We consider a vacuum static spacetime in a finite size cavity. On the boundary, we specify a metric and a finite constant local temperature $T$. No spherical or any other spatial symmetry is assumed. We show that (i) inside a cavity, only a black hole or flat spacetime are possible, whereas a curved horizonless regular space-time is excluded, (ii) in the limit when the horizon area shrinks, the Hawking temperature diverges, (iii) for the existence of a black hole, $T$ should be high enough. When $T\rightarrow \infty $, a black hole phase is favorable thermodynamically. Our consideration essentially uses the coordinate system introduced by Israel in his famous proof of the uniqueness theorem.