Vacuum Cosmological Models in Einstein and Barber Theories

Abstract

An attempt has been made to solve the field equations with perfect fluid in an inhomogeneous space-time governed by the metric $$ds^2 = dt^2 - dx^2 - y^2 - dz^2 + f\left( {t - x,y,z} \right)\left( {dt - dx} \right)^2$$ in both Einstein and Barber's theories of gravitation. It is shown here that in both the theories the field equations are reducible to a Laplace equation and the perfect fluid distribution does not survive. Moreover all the solutions represent plane gravitational wave and the vacuum models in both the theories can be constructed by an arbitrary harmonic function iny and z coordinates.