Mass quantization of the Schwarzschild black hole - art. no. 024009

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kuchar-Brown variables and obtain its energy eigenstates. Con sistent solutions vanish in the exterior of the Kruskal manifold and are no nvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectru m, depending on one quantum number which determines the Arnowitt-Deser-Misn er mass of the black hole according to a relation conjectured long ago by B ekenstein M similar to root nM(p). If attention is restricted only to these quantized energy states, a black hole is described not only by its mass bu t also by its parity. States of indefinite parity do not admit a quantized mass spectrum. [S0556-2821(99)01914-1].