Negative modes and the thermodynamics of Reissner-Nordstr\"om black holes

Understand

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.