DIMENSIONALLY CONTINUED BLACK-HOLES

Static, spherically symmetric solutions of the held equations for a pa rticular dimensional continuation of general relativity with a negativ e cosmological constant are studied. The action is, in odd dimensions, the Chern-Simons form for the anti-de Sitter group and, in even dimen sions, the Euler density constructed with the Lorentz part of the anti -de Sitter curvature tenser. Both actions are special cases of the Lov elock action, and they reduce to the Hilbert action (with a negative c osmological constant) in the lower dimensional cases D = 3 and D = 4. Exact black hole solutions characterized by mass (M) and electric char ge (Q) are found. In odd dimensions a negative cosmological constant i s necessary to obtain a black hole, while in even dimensions both asym ptotically hat and asymptotically anti-de Sitter black holes exist. Th e causal structure is analyzed and the Penrose diagrams are exhibited. The curvature tenser is singular at the origin for all dimensions gre ater than three. In dimensions of the form D=4k, 4k-1, the number of h orizons may be zero, one, or two, depending on the relative values of M and Q, while for a negative mass there is no horizon for any real va lue of Q. In the other cases, D=4k + 1, 4k+2, both naked and dressed s ingularities with a positive mass exist. As in three dimensions, in al l odd dimensions anti-de Sitter space appears as a ''bound state'' of mass M = -1, separated hem the continuous spectrum (M greater than or equal to O) by a gap of naked curvature singularities. In even dimensi ons anti-de Sitter space has sere mass. The analysis is Hamiltonian th roughout, considerably simplifying the discussion of the boundary term s in the action and the thermodynamics. The Euclidean black hole has t he topology R(2) X S-D-2. Evaluation of the Euclidean action gives exp licit expressions for all the relevant thermodynamical parameters of t he system. The entropy, defined as a surface term in the action coming from the horizon, is shown to be a monotonically increasing function of the black hole radius, different from the area for D > 4.