Cylindrical wave solutions of the field equations representing zero-rest-mass scalar fields and those of lichnerowicz's « total radiation » in a generalized Einstein-Rosen space-time

Abstract

Lichnerowicz (1960), by using a property of the Riemann tensor, has given the field equations, Rij=ϱwiwj, wiwi=0, ϱ being a scalar and has termed them as representing a state of « total radiation ». Recently Rao (1970) derived these field equations under a geometrical relation which as stated by him imposes on the Rieman tensor a severe restriction, and he obtained a class of exact solutions of the above field equations corresponding to the cylindrically symmetric space-time with two degrees of freedom. The present authors, in this paper, have obtained exact wave solutions of the field equations representing zero-rest-mass scalar field in the generalized Einstein-Rosen space-time, and it has been shown that by a suitable choice of the scalar field, the field equations considered by Lichnerowicz and Rao can be deduced without imposing any condition on the geometrical nature of the Riemann tensor. Finally a method is given by which most general solutions of these field equations, can be generated from those of the empty space field equations. It is further shown that the solutions of Rao (1960) are only a special case of those found in this paper.