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ISRN Astronomy and Astrophysics
Volume 2012 (2012), Article ID 178561, 6 pages
http://dx.doi.org/10.5402/2012/178561
Research Article

A Nonaxisymmetric Solution of Einstein’s Equations Featuring Pure Radiation from a Rotating Source

1Mathematics and Statistics Department, University of Otago, Dunedin, New Zealand
221 Rowbank Way, Loughborough, Leicestershire LE11 4AJ, UK

Received 7 January 2012; Accepted 8 February 2012

Academic Editors: H. Dehnen and N. Fornengo

Copyright © 2012 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.

Abstract

A special nonaxisymmetric solution of Einstein’s equations is derived, representing pure radiation from a rotating isolated source. The spacetime is assumed to be algebraically special having a multiple null eigenvector of the Weyl tensor forming a geodesic, shear-free, diverging, and twisting congruence 𝐤 . Employing a complex null tetrad involving the vector 𝐤 , the Ricci tensor, density of the radiation, divergence, and twist are calculated for the derived metric. A particular (nonaxisymmetric) subcase is shown to be flat at infinity and to contain the axisymmetric radiating Kerr metric, derived by Kramer and separately by Vaidya and Patel, as a special case. The spacetime is of Petrov type II and without Killing vectors.