Stationary Vacuum Black Hole Solutions

We generalize the concept of rod structure for stationary axisymmetric solutions in vacuum and introduce the basic black hole solutions belonging to this class focusing on their physical properties. They include black holes with a non-trivial horizon topology as well as balanced multi-horizon configurations. In the last section we discuss some important properties of the stationary and axisymmetric Einstein equations in vacuum such as their sigma-model structure and their representation by means of the Ernst and the twist potentials.