Abstract
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.
Highlights
A Central Mass in a Stationary Vacuum without Spherical or Axial SymmetryMathematics and Statistics Department, University of Otago, Dunedin, New Zealand
We present a special solution of Einstein’s equations which can be described as a stationary vacuum spacetime with a central mass singularity without spherical or axial symmetry
The field equations for a vacuum metric that admits a geodesic, shear-free, and diverging null congruence k were obtained by Kerr [1] and I
Summary
Mathematics and Statistics Department, University of Otago, Dunedin, New Zealand. 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 is algebraically special. The properties of the metric are calculated. 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 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
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