Classification of vacuum classes of plane fronted gravitational waves via proper conformal vector fields in f(R) gravity

Abstract

In this paper, we have studied proper conformal vector fields of pp-wave space-times in the [Formula: see text] theory of gravity using algebraic and direct integration techniques. From this study, we found that a very special class of pp-waves known as plane fronted gravitational waves (GWs) is a solution in the [Formula: see text] theory of gravity. In order to find proper conformal vector fields, plane GWs are further classified in ten cases. Studying each case in detail it turns out that in two cases proper conformal vector fields exist while in the rest of eight cases, conformal vector fields become homothetic vector fields.