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Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence

Marcello Ortaggio
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Abstract

We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.

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Marcello Ortaggio. 2007-08-30. Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence. https://arxiv.org/abs/gr-qc/0701036

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