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arXiv · 1001.3629

Complete classification of second-order symmetric spacetimes

O F Blanco·M Sánchez·J M M Senovilla
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Abstract

As a difference with the positive-definite Riemannian case, in the Lorentzian case there exists proper second-order symmetric spacetimes, i.e., those with vanishing second covariant derivative of the Riemannian tensor ($R_{λμνρ;α;β}=0$) which are not locally symmetric ($R_{λμνρ;α}\neq 0$). In fact, they lie in the class of Brinkmann metrics, and include some known plane waves. Our purpose is to classify these spacetimes in the 4 dimensional case.

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O F Blanco, M Sánchez, J M M Senovilla. 2010-01-20. Complete classification of second-order symmetric spacetimes. https://doi.org/10.1088/1742-6596%2F229%2F1%2F011001

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