Invariant solutions and conservation laws of Einstein field equations in non-comoving radiation fields

The exact non-static accelerating solutions of Einstein field equations in non-comoving pure radiation fields, corresponding to an indefinite non-degenerate metric in cartesian coordinates, are obtained. The gravitational field is of Petrov type D and the considered spacetime is not conformally flat. Lie symmetry method is used for symmetry reduction of nonlinear partial differential equations and for finding the exact solutions, comprising both arbitrary functions and known analytic functions. Conservation laws are obtained by using multiplier approach. The graphical representations of solutions are shown by considering different possibilities of the arbitrary functions.