A Twisting Electrovac Solution of Type II with the Cosmological Constant

Abstract

An exact solution of the current-free Einstein-Maxwell equations with the cosmological constant is presented. It is of Petrov type II, and its double principal null vector is geodesic, shear-free, expanding, and twisting. The solution contains five constants. Its electromagnetic field is non-null and aligned. The solution admits only one Killing vector and includes, as special cases, several known solutions.Comment: 4 pages, LaTeX 2e, no figures. The present (second) version, identical to that published in General Relativity and Gravitation, is derived from the first version by presenting the admitted Killing vector, and by adding the last paragraph, two footnotes (here Footnotes 1 and 3), and two references (here Refs. [3,4]