Pure radiation fields admitting nontrivial null symmetries

Abstract

The sixteen types of geometrical symmetries corresponding to the continuous groups of collineations and motions generated by a null vector n are considered. The common propagation vector of a pure electromagnetic radiation field and a pure gravitational radiation field is chosen to be n. For such radiation fields all the sixteen symmetries are expressed in terms of the Newman–Penrose (NP) spin coefficients and then it is shown that when n is a gradient field there are only five independent symmetries. The existence of these five nontrivial null symmetries is established by finding exact solutions of Einstein–Maxwell field equations when n satisfies freedom conditions and when l of the NP null tetrad (l, m, m̄, n) is shear-free. Thus a class of space-times of pure radiation fields that admit (i) a Ricci collineation which is not a curvature collineation (CC), (ii) a CC which is not a special curvature collineation (SCC), (iii) a SCC which is not an affine collineation (AC), (iv) an AC which is not a motion, and (v) a motion is determined.