English

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 dd-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell (p+1)(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)(p+1)-form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily CSICSI and the (p+1)(p+1) form is VSIVSI. 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

R2 v1 2026-06-22T19:18:42.863Z