Generalized plane gravitational waves of weakened field equations in general relativity

In this paper, we propose to obtain a generalized plane gravitational waves in a set of five vacuum weakened field equations in the space-time introduced by Takeno (1961). These vacuum field equations have been suggested as alternatives to the Einstein vacuum field equations of general relativity. Physical significance of modified gravitational waves for the space-time is obtained. The dispersion relation for gravitational waves in vacuo is derived. We have obtained some useful results in the form of theorems under the curvature properties with conclusions.