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∈1,2,,[(d-1)/2] which possess a unique globally AdS vacuum. The transverse sections of these solutions are d-2 surfaces of constant curvature γ, normalized to γ=±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 [(d-1)/2] different conformal field theories at the boundary.