# Gyratons in the Robinson-Trautman and Kundt classes

## TL;DR

This paper corrects previous errors and demonstrates the existence of gyratonic solutions in Robinson-Trautman and Kundt classes across all dimensions, expanding understanding of these spacetimes in general relativity.

## Contribution

It provides the first explicit family of gyratonic solutions in Robinson-Trautman and Kundt spacetimes for any dimension ≥ 3, correcting earlier misconceptions.

## Key findings

- Gyratons exist in all twist-free, shear-free geometries.
- Explicit canonical metrics for these solutions are derived.
- Solutions are valid in arbitrary dimensions ≥ 3.

## Abstract

In our previous paper [Phys. Rev. D 89 (2014) 124029], cited as [1], we attempted to find Robinson-Trautman-type solutions of Einstein's equations representing gyratonic sources (matter field in the form of an aligned null fluid, or particles propagating with the speed of light, with an additional internal spin). Unfortunately, by making a mistake in our calculations, we came to the wrong conclusion that such solutions do not exist. We are now correcting this mistake. In fact, this allows us to explicitly find a new large family of gyratonic solutions in the Robinson-Trautman class of spacetimes in any dimension greater than (or equal to) three. Gyratons thus exist in all twist-free and shear-free geometries, that is both in the expanding Robinson-Trautman and in the non-expanding Kundt classes of spacetimes. We derive, summarize and compare explicit canonical metrics for all such spacetimes in arbitrary dimension.