Negative modes and the thermodynamics of Reissner-Nordström black holes

Details Negative modes and the thermodynamics of Reissner-Nordström black holes Negative modes and the thermodynamics of Reissner-Nordström black holes

2008-12-09

arxiv.org/abs/0812.1767v2

Phys. Rev. D 79, 064006 (2009)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, 1 figure; v2 minor changes to fit published version

Scientific paper

10.1103/PhysRevD.79.064006

We analyse the problem of negative modes of the Euclidean section of the Reissner-Nordstr\"om black hole in four dimensions. We find analytically that a negative mode disappears when the specific heat at constant charge becomes positive. The sector of perturbations analysed here is included in the canonical partition function of the magnetically charged black hole. The result obeys the usual rule that the partition function is only well-defined when there is local thermodynamical equilibrium. We point out the difficulty in quantising Einstein-Maxwell theory, where the so-called conformal factor problem is considerably more intricate. Our method, inspired by hep-th/0608001, allows us to decouple the divergent gauge volume and treat the metric perturbations sector in a gauge-invariant way.

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