We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole
spacetimes in which the two-sphere has been replaced by a surface Sigma of
constant negative or zero curvature. When horizons exist, the spacetimes are
black holes with an asymptotically locally anti-de Sitter infinity, but the
infinity topology differs from that in the asymptotically Minkowski case, and
the horizon topology is not S^2. Maximal analytic extensions of the solutions
are given. The local Hawking temperature is found. When Sigma is closed, we
derive the first law of thermodynamics using a Brown-York type quasilocal
energy at a finite boundary, and we identify the entropy as one quarter of the
horizon area, independent of the horizon topology. The heat capacities with
constant charge and constant electrostatic potential are shown to be positive
definite. With the boundary pushed to infinity, we consider thermodynamical
ensembles that fix the renormalized temperature and either the charge or the
electrostatic potential at infinity. Both ensembles turn out to be
thermodynamically stable, and dominated by a unique classical solution.Comment: 25 pages, REVTeX v3.1, contains 5 LaTeX figures. (Typos corrected,
references and minor comments added. To be published in Phys. Rev. D.
