On the Quantum Levels of Isolated Spherically Symmetric Gravitational Systems

Preprint

29 May 1996

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.gr-qc/9605038

Abstract

The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the proper time \tau of obsevers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr-Sommerfeld quantisation in atomic physics. The two approaches can be related by postulating periodic boundary conditions in time for the plane waves and by identifying the period \Delta in real time with the period \Delta_H= 8\pi GM/c^3 in Euclidean time. This yields the mass spectrum M_n=(1/2)\sqrt{n}m_P, n=1,2,... .

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All Related Versions

Version 1, 1996-05-17, ArXiv
Version 2, 1996-05-29, ArXiv
Published version: Physics Letters B, 385 (1-4), 75.

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