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I read the book The global nonlinear stability of the minkowski space by Christodoulou, D., and Klainerman, S.

In the Chapter I, Page 10 it says:

“However, it remains questionable whether there exists any nontrivial6 solution of the field equations that satisfies the Penrose requirements. Indeed, his regularity assump­tions translate into fall-off conditions of the curvature that may be too stringent and thus may fail to be satisfied by any solution that would allow gravitational waves.”

So I am curious about if anyone had found such solutions above that is non-stationary asymptotically flat and geodesic completeness.

Thank you.

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    $\begingroup$ A geon solution? $\endgroup$ – Slereah Oct 15 '17 at 15:31

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