Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds

Understand

The variational problem of gravity theories is directly related to black hole thermodynamics.

• For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics.
• We show that this connection holds well beyond asymptotically AdS black holes.
• In particular, we formulate the variational problem for $\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'.