Distorted vacuum black holes in the canonical ensemble

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 $T\to \infty$, 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.

6 pages. Eq. 8 written more accurately. Matches published version

References in corpus (1)

• Dirty black holes: Spacetime geometry and near-horizon symmetries