Abstract

The subtle nature of energy in General Relativity means that naive attempts to use energy to study stability or instability are bound to fail. On the other hand, at the linear level, in an asymptotically flat background, an energy-type quantity can be constructed whose positivity properties are linked to the stability of the background. This was done in a recent paper by Hollands and Wald.

I will present a generalization of this work to the case where matter and charge are present. In the first part of the talk I will briefly discuss the covariant phase-space derivation of the first law in the theory under consideration, as this arises naturally through the construction of Hollands and Wald. Next I will construct the appropriate “energy”, and discuss the properties which make it appropriate for the study of stability. One of the key properties is the positivity of the flux of this energy across null infinity, but in order to discuss this, an appropriate notion of “asymptotic flatness” must be given, and its (linear) stability established; an indication of how this is done will be given in the next part of my talk. Finally, I will discuss an application of this work to charged black branes, which establishes that, if the brane is thermodynamically unstable and sufficiently extended, then it is classically unstable.