1306.6087 (Joe Keir)

Stability, Instability, Canonical Energy and Charged Black Holes    [PDF]

Joe Keir

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.

View original: http://arxiv.org/abs/1306.6087