Conformally flat travelling plane wave solutions of Einstein equations

Abstract

We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase $\xi =\omega \tau -\mathbf{qx}$, where $\tau$ is the conformal time. We show that ideal fluid Einstein equations and scalar fields with exponential self-interaction have solutions of this form. We consider in more detail the source depending on $\xi$ with $\omega =|\mathbf{q}|$ 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 such a source of the energy-momentum.

substantially changed version,18 pages

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