A spacetime for which the Karlhede invariant classification requires the fourth covariant derivative of the Riemann tensor

Abstract

It is shown that the conformally flat radiation metric found by Wils (1989) requires the fourth covariant derivative of the Riemann tensor for the Karlhede classification to terminate. This contradicts a widely held opinion that the true upper bound is three. The metric can admit at most one Killing vector and/or a homothety.

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