Higher dimensional black holes

Black hole solutions to Einstein's equations are examined in asymptotically flat N + 1 dimensional space-times. Generalizations of Schwarzschild and Reissner-Nordstroem solutions are examined in a discussion of static black holes in N + 1 dimensions. A new family of solutions is found which describe spinning black holes in higher dimensional space-times. In many respects these new solutions are similar to the familiar Kerr and Schwarzschild metrics which are recovered for N = 3. One exceptional case though is that for N ≥ 5 black holes with a fixed mass may have arbitrarily large angular momentum. Next the Majumdar-Papapetrou solutions of the Einstein-Maxwell equations are generalized to higher dimensions. These new solutions are then used to construct black hole solutions in which the extra dimensions are compactified on a torus. Conjectures about similar constructions for the vacuum Einstein equations are also discussed