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)\times 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 membrane-like 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-Maxwell-dilaton theory.

Figures (6)

• Figure 1: Rod structure of the 5D Schwarzschild black hole solution.
• Figure 2: Rod structure of an $N$-Schwarzschild black hole solution.
• Figure 3: Rod structure of the background spacetime of (\ref{['general metric']}).
• Figure 4: Rod structure of the two-black hole solution.
• Figure 5: The horizon of the left black hole as represented by the quarter-circle $0\leq\theta\leq\frac{\pi}{2}$, with proper radius $\sqrt{g_{\theta\theta}}$, for (a) $w=5$, (b) $w=0.5$, and (c) $w=0.05$. The jagged lines denote the conical singularities stretching between the two black holes.