Is the semi-classical analysis valid for extreme black holes?

Details Is the semi-classical analysis valid for extreme black holes? Is the semi-classical analysis valid for extreme black holes?

2003-06-09

arxiv.org/abs/gr-qc/0306030v3

Phys.Lett. A320 (2003) 83-94

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex file, 10 pages. A new section was included. New title, new references and others minors modifications. To appear in Phys

Scientific paper

The surface gravity for the extreme Reissner-Nordstr\"om black hole is zero suggesting that it has a zero temperature. However, the direct evaluation of the Bogolubov's coefficients, using the standard semi-classical analysis, indicates that the temperature of the extreme black hole is ill definite: the Bogolubov's coefficients obtained by performing the usual analysis of a collapsing model of a thin shell, and employing the geometrical optical approximation, do not obey the normalization conditions. We argue that the failure of the employement of semi-classical analysis for the extreme black hole is due to the absence of orthonormal quantum modes in the vicinity of the event horizon in this particular case.

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