Static Vacuum Black Hole Solutions

We consider static axisymmetric solutions to the five-dimensional Einstein equations in vacuum which possess two orthogonal spacelike Killing vectors. This class represents a generalization of the four-dimensional Weyl solutions, however providing much greater variety of black holes. The solutions are associated formally with a collection of rod sources of the gravitational potential called rod structure. We demonstrate explicitly how the various black hole solutions arise assuming particular combinations of rod sources and how we can construct black hole spacetimes with a non-trivial topology.