Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory
General Relativity and Quantum Cosmology
2017-05-03 v2
Abstract
We consider -dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell -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 -form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily and the form is . Finally, a general coordinate form of solutions and a reduction of the field equations are discussed.
Keywords
Cite
@article{arxiv.1704.04827,
title = {Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory},
author = {Martin Kuchynka and Alena Pravdova},
journal= {arXiv preprint arXiv:1704.04827},
year = {2017}
}
Comments
11 pages, minor changes