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Class. Quantum Grav. 9 (February 1992) 457-473

Energy spectrum of a quantum black hole

J Louko and B F Whiting
Theor. Phys. Inst., Alberta Univ., Edmonton, Alta., Canada

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.

URL: stacks.iop.org/0264-9381/9/457
DOI: 10.1088/0264-9381/9/2/011

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