Higher dimensional Chern-Simons theories and topological black holes

It has been recently pointed out that black holes of constant curvature with a “chronological singularity” can be constructed in any spacetime dimension. These black holes share many common properties with the 2+1 black hole. In this contribution we give a brief summary of these new black holes and consider them as solutions of a Chern-Simons gravity theory. We also provide a brief introduction to some aspects of higher dimensional Chern-Simons theories. I. THE TOPOLOGICAL BLACK HOLE A topological black hole in n dimensions can be constructed by making identifications along a particular Killing vector on n dimensional anti-de Sitter space, just as the 2+1 black hole is constructed from 3 dimensional anti-de Sitter space. This procedure can be summarized as follows. Consider the n dimensional anti-de Sitter space − x20 + x21 + · · ·+ x2n−2 + x2n−1 − x2n = −l, (1) and consider the boost ξ = (r+/l)(xn−1∂n + xn∂n−1) with norm ξ 2 = (r +/l )(−xn−1 + x2n). For ξ = r +, one has the null surface,