  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.
