LAUSR

We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase [Formula: see text], where [Formula: see text] is the conformal time. We show that ideal fluid Einstein equations and scalar fields with exponential self-interaction have solutions of the form of traveling fluid plane waves. We consider in more detail the source depending on [Formula: see text] with [Formula: see text] describing models of a massless scalar field, electromagnetic field and relativistic particles with space-time depending mass density. We obtain explicit conformally flat metrics solving Einstein equations with a source of the energy–momentum moving with a speed of light.