Black holes with topologically nontrivial AdS asymptotics

Asymptotically locally AdS black hole geometries of dimension $d>~3$ are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer $k\in \{1,2,\dots ,\left[\right(d-1)/2]\}$ which possess a unique globally AdS vacuum. The transverse sections of these solutions are $d-2$ surfaces of constant curvature $\gamma ,$ normalized to $\gamma =\pm 1,0$ allowing for different topological configurations. The thermodynamic analysis of these solutions reveals that the presence of a negative cosmological constant is essential to ensure the existence of stable equilibrium states. In addition, it is shown that these theories are holographically related to $\left[\right(d-1)/2]$ different conformal field theories at the boundary.