A Central Mass in a Stationary Vacuum without Spherical or Axial Symmetry

A vacuum spacetime with a central mass is derived as a stationary solution to Einstein's equations. The vacuum metric has a geodesic, shear-free, expanding, and twisting null congruence k and thus is algebraically special. The properties of the metric are calculated. In particular, it is shown that the spacetime has an event horizon inside which there is a black hole. The metric is neither spherically nor axially symmetric. It is therefore in interesting contrast with the majority of metrics featuring a central mass which have one or more of these symmetry properties. The metric reduces to the Schwarzschild case when a certain parameter is set to zero.