Mass quantization of the Schwarzschild black hole

Cenalo Vaz and Louis Witten
Phys. Rev. D 60, 024009 – Published 14 June 1999
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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 MnMp. 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.

  • Received 19 November 1998

DOI:https://doi.org/10.1103/PhysRevD.60.024009

©1999 American Physical Society

Authors & Affiliations

Cenalo Vaz*

  • Department of Physics, The Johns Hopkins University, Baltimore, Maryland 21218

Louis Witten

  • Department of Physics, The University of Cincinnati, Cincinnati, Ohio 45221-0011

  • *On leave of absence from the Universidade do Algarve, Faro, Portugal. Email address: cvaz@haar.pha.jhu.edu
  • Email address: witten@physunc.phy.uc.edu

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Vol. 60, Iss. 2 — 15 July 1999

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