Thermodynamics of Einstein-Proca AdS Black Holes

Understand

We study static spherically-symmetric solutions of the Einstein-Proca equations in the presence of a negative cosmological constant.

• We show that the theory admits solutions describing both black holes and also solitons in an asymptotically AdS background.
• Interesting subtleties can arise in the computation of the mass of the solutions and also in the derivation of the first law of thermodynamics.
• We make use of holographic renormalisation in order to calculate the mass, even in cases where the solutions have a rather slow approach to the asymptotic AdS geometry.