Mass Quantization of the Schwarzschild Black Hole

Details Mass Quantization of the Schwarzschild Black Hole Mass Quantization of the Schwarzschild Black Hole

1998-11-18

arxiv.org/abs/gr-qc/9811062v2

Phys.Rev. D60 (1999) 024009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Change in eq. (13). Factors of 4 cleaned up. Refs. added

Scientific paper

10.1103/PhysRevD.60.024009

We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild black hole in Kucha\v r-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are non-vanishing 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 (ADM) mass of the black hole according to a relation conjectured long ago by Bekenstein, $M \sim \sqrt{n}M_p$. 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.

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