Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are e?‘?e?‘?-waves. Brinkmann's result has been generalized to include the conformally invariant source terms. It has been shown that [4] if $g_{ik}$ and $overline{g}_{ik}$ ($=e??”^{-2}g_{ik}$, e??”: a scalar function), are distinct metrics having the same Einstein tensor, $G_{ik}=overline{G}_{ik}$, then both represent (generalized) $pp$-waves and $e??”_{i}$ is a null convariantly constant vector of $g_{ik}$. Thus $pp$-waves are the only candidates which yield conformally related nontrivial solutions of $G_{ik}=T_{ik}=overline{G}_{ik}$, with $T_{ik}$ being conformally invariant source.
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