Table of Contents
ISRN Astronomy and Astrophysics
Volume 2013 (2013), Article ID 470634, 4 pages
Research Article

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

Mathematics and Statistics Department, University of Otago, Dunedin, New Zealand

Received 15 March 2013; Accepted 22 May 2013

Academic Editors: H. Dehnen and D. Kieda

Copyright © 2013 William Davidson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.