Stability, Instability, Canonical Energy and Charged Black Holes

Abstract

We use the canonical energy method of Hollands and Wald to study the stability properties of asymptotically flat, stationary solutions to a very general class of theories, consisting of a set of coupled scalar fields and p-form gauge fields, minimally coupled to gravity. We find that, provided certain very weak assumptions are made on the coupling coefficients, the canonical energy method can be extended to this class of theories. In particular, we construct a quadratic form E on initial data perturbations, with the properties that E > 0 on all perturbations indicates stability, while E < 0 on some perturbation indicates instability. Furthermore, we show that the conditions needed for the existence of E allow for a stable definition of asymptotic flatness. Finally, we extend the proof of the Gubser-Mitra conjecture, given by Hollands and Wald, to this class of theories. In particular, this shows that for sufficiently extended, charged black brane solutions to such theories, thermodynamic instability implies dynamical instability.

31 pages

References in corpus (7)

• An instability of higher-dimensional rotating black holes
• Gravitational instability of an extreme Kerr black hole
• Ultraspinning instability of rotating black holes
• Note on the First Law with p-form potentials
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
• Ultraspinning instability: the missing link
• First Law of p-brane Thermodynamics

Cited by in corpus (10)

• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• Black hole thermodynamics in the presence of nonlinear electromagnetic fields
• Superradiant instabilities of asymptotically anti-de Sitter black holes
• Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
• Instabilities of extremal rotating black holes in higher dimensions
• Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
• Black hole thermodynamics, stringy dualities and double field theory
• Canonical energy and hairy AdS black holes
• Dynamical entropy of charged black objects
• A little hair can make a big difference: thermodynamic stability of quasi-bald asymptotically-flat black holes