Stability, Instability, Canonical Energy and Charged Black Holes

TL;DR

This paper extends the canonical energy method to a broad class of gravity theories with scalar and gauge fields, establishing criteria for stability and linking thermodynamic and dynamical instabilities in charged black branes.

Contribution

It generalizes the canonical energy approach to new theories and proves the Gubser-Mitra conjecture for extended charged black branes within this framework.

Findings

Canonical energy method extended to scalar and p-form gauge fields

Positive canonical energy indicates stability, negative indicates instability

Thermodynamic instability implies dynamical instability for charged black branes

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.