Hamiltonian thermodynamics of d-dimensional (d=4 and d>4) Reissner-Nordstr\"om anti-de Sitter black holes with spherical, planar, and hyperbolic topology

Understand

The Hamiltonian thermodynamics formalism is applied to the general $d$-dimensional Reissner-Nordstr\"om-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology.

• After writing its action and performing a Legendre transformation, surface terms are added in order to guarantee a well defined variational principle with which to obtain sensible equations of motion, and also to allow later on the thermodynamical analysis.
• Then a Kucha\v{r} canonical transformation is done, which changes from the metric canonical coordinates to the physical parameters coordinates.
• Again a well defined variational principle is guaranteed through boundary terms.