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

## TL;DR

This paper classifies Weyl type N solutions with null electromagnetic fields in higher-dimensional Einstein-Maxwell theory, showing they are aligned, belong to the Kundt class, and possess specific geometric and invariant properties.

## Contribution

It proves that such solutions are necessarily aligned, geodetic, shear-free, and belong to the Kundt class, extending understanding of null electromagnetic fields in higher-dimensional gravity.

## Key findings

- Solutions are aligned and belong to the Kundt class.
- Weyl type N spacetimes with null Maxwell fields are CSI and VSI.
- A general coordinate form and field equation reduction are provided.

## 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.