Plane Wave Solutions of Weakened Field Equations in Generalized Space-time

Abstract

Various attempts have been made to obtain the plane wave solutions of Weakened Field Equations (abbreviated as WFE) suggested by Kilmister and Newman^[1] (1961),  and Rund^[3] (1967).In this paper we propose to obtain the plane wave solutions of the WFE in the sense of Takeno^[4] (1961). For this purpose we have chosen a generalized metric used by  K. B. Lal and Shafiullah^[5] and obtained the conditions under which these WFE are satisfied. The method used is on the lines of D.Lovelock^[7] and the results are stated in the forms of theorems. The physical significance of the gravitational waves is also discussed.