Mass quantization of the Schwarzschild black hole

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kuchař-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing 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 spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M∼√nM_p. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.