Black Holes with Polyhedral Multi-String Configurations

We find exact solutions of the Einstein equations which describe a black hole pierced by infinitely thin cosmic strings. The string segments enter the black hole along the radii and their positions coincide with the symmetry axes of a regular polyhedron. Each string produces an angle deficit proportional to its tension, while the metric outside the strings is locally Schwarzschild one. There are three configurations corresponding to tetrahedra, octahedra and icosahedra where the number of string segments is 14, 26 and 62, respectively. There is also a "double pyramid" configuration where the number of string segments is not fixed. There can be two or three independent types of strings in one configuration. Tensions of strings belonging to the same type are equal. Analogous polyhedral multi-string configurations can be combined with other spherically symmetric solutions of the Einstein equations.