Mass quantization of the Schwarzschild black hole
- 14 June 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 60 (2) , 024009
- https://doi.org/10.1103/physrevd.60.024009
Abstract
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 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.
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