Invariant solutions of Einstein field equations in pure radiation fields

Abstract

The exact static accelerating solutions of Einstein’s equations in the non-comoving pure radiation fields, with an indefinite non-degenerate stationary metric in cylindrical coordinates, are obtained. The considered space-time is of Petrov type I and is not conformally flat. Moreover, the classical symmetry method is used for symmetry reduction and finding the solutions in terms of hyperbolic functions. The conservation laws are found by using the multiplier approach.