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On quantization of black holes. (English) Zbl 0956.83531

Summary: A black hole model with a self-gravitating charged spherically symmetric thin dust shell as a source is considered. A Schrödinger-type equation for such a model is derived. This equation appears to be a difference equation. A theory of such an equation is developed and its general solution is found and studied in detail. A discrete spectrum of bound state energy levels is obtained. All the eigenvalues appear to be infinitely degenerate. The ground state wave functions are evaluated explicitly. Quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and for nearly extreme Reissner-Nordstróm black holes. The above-mentioned infinite degeneracy of the mass (energy) eigenvalues may be helpful in resolving the well-known information paradox in black hole physics.

MSC:

83C57 Black holes
83C45 Quantization of the gravitational field
80A10 Classical and relativistic thermodynamics
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