Multi-black-hole solutions in five dimensions

Abstract

Using a recently developed generalized Weyl formalism, we construct an asymptotically flat, static vacuum Einstein solution that describes a superposition of multiple five-dimensional Schwarzschild black holes. The spacetime exhibits a U(1) × U(1) rotational symmetry. It is argued that for certain choices of parameters the black holes are collinear and so may be regarded as a five-dimensional generalization of the Israel-Khan solution. The black holes are kept in equilibrium by membranelike conical singularities along the two rotational axes; however, they still distort one another by their mutual gravitational attraction. We also generalize this solution to one describing multiple charged black holes, with fixed mass-to-charge ratio, in Einstein-Max well-dilaton theory. æ 2003 The American Physical Society.