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

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.