Energy spectrum of a quantum black hole

Abstract

The authors discuss a minisuperspace path integral for the partition function of a Schwarzschild black hole in thermal equilibrium within a finite spherical box. Building on a novel classical variational principle, they define and evaluate a partition function using a non-trivial complex integration contour. The partition function solves exactly the relevant differential equation related to the Wheeler-DeWitt equation, and it has the desired semiclassical behaviour indicating in particular thermodynamical stability. For a given size of the box, the density-of-states is non-vanishing only in a finite energy interval whose upper end is twice as high as would be classically expected without negative temperatures.