Dimensionally continued black holes.

Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are studied. The action is, in odd dimensions, the Chern-Simons form for the anti-de Sitter group and, in even dimensions, the Euler density constructed with the Lorentz part of the anti-de Sitter curvature tensor. Both actions are special cases of the Lovelock action, and they reduce to the Hilbert action (with negative cosmological constant) in the lower dimensional cases D = 3 and D = 4. Exact black hole solutions characterized by mass (M) and electric charge (Q) are found. In odd dimensions a negative cosmological constant is necessary to obtain a black hole, while in even dimensions, both asymptotically flat and asymptotically anti-de Sitter black holes exist. The causal structure is analyzed and the Penrose diagrams are exhibited. The curvature tensor is singular at the origin for all dimensions greater than Electronic address: [email protected]