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arXiv · 1704.04827

Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory

Martin Kuchynka·Alena Pravdova
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Abstract

We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the corresponding spacetime and the electromagnetic field share the same \textit{aligned null direction} (AND). Moreover, this AND is geodetic, shear-free, non-expanding and non-twisting and hence Einstein-Maxwell equations imply that Weyl type N spacetimes with a null Maxwell $(p+1)$-form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily $CSI$ and the $(p+1)$ form is $VSI$. Finally, a general coordinate form of solutions and a reduction of the field equations are discussed.

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Martin Kuchynka, Alena Pravdova. 2017-04-16. Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory. https://doi.org/10.1007/s10714-017-2234-7

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