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

F. G. Alvarenga·A. B. Batista·J. C. Fabris·G. T. Marques
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Abstract

The surface gravity for the extreme Reissner-Nordström 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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F. G. Alvarenga, A. B. Batista, J. C. Fabris, G. T. Marques. 2003-11-14. Is the semi-classical analysis valid for extreme black holes?. https://doi.org/10.1016/j.physleta.2003.11.010

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