Negative modes and the thermodynamics of Reissner-Nordström black holes

Abstract

We analyse the problem of negative modes of the Euclidean section of the Reissner-Nordström 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.

arXiv comment24 pages, 1 figure; v2 minor changes to fit published version

References in corpus (19)

• General relativity as an effective field theory: The leading quantum corrections
• Black Strings and p-Branes are Unstable
• The evolution of unstable black holes in anti-de Sitter space
• Duality between Electric and Magnetic Black Holes
• Classical and Thermodynamic Stability of Black Branes
• Instabilities of Black Strings and Branes
• Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter
• Unstable Horizons
• Ricci flow and black holes
• High and Low Dimensions in The Black Hole Negative Mode
• Stable Black Strings in Anti-de Sitter Space
• Homogeneous Modes of Cosmological Instantons
• Closed Universes from Cosmological Instantons
• Classical Stability of Charged Black Branes and the Gubser-Mitra Conjecture
• On d=4,5,6 Vacua with 8 Supercharges
• New stable phase of non-uniform charged black strings
• The Power of Action: "The" Derivation of the Black Hole Negative Mode
• Semi-classical stability of AdS NUT instantons
• Negative modes of Schwarzschild black hole in Einstein-Gauss-Bonnet Theory

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