# From polarized gravitational waves to analytically solvable electromagnetic beams

## TL;DR

This paper explores the connection between gravitational waves and electromagnetic beams, using the classical double copy conjecture to construct analytically solvable vortex electromagnetic fields from gravitational solutions, with applications to laser physics.

## Contribution

It introduces a method to generate solvable electromagnetic vortex fields from gravitational wave solutions via the classical double copy, highlighting the role of conformal symmetry and Niederer transformations.

## Key findings

- Constructed electromagnetic vortex fields with solvable Lorentz force equations.
- Linked gravitational wave solutions to laser beam models with focusing properties.
- Presented new examples of analytically solvable electromagnetic beams.

## Abstract

Using the correspondence between solutions of gravitational and gauge theories (the so-called classical double copy conjecture) some electromagnetic fields with vortices are constructed, for which the Lorentz force equations are analytically solvable. The starting point is a certain class of plane gravitational waves exhibiting the conformal symmetry. The notion of the Niederer transformation, crucial for the solvability, is analysed in the case of the Lorentz force equation on the curved spacetimes as well as its derivation by means of integrals of motion (associated with conformal generators preserving these vortices) is presented. Furthermore, some models discussed recently in the context of the intense laser beams are constructed from their gravitational counterparts, with the special emphasis put on the focusing property, and new solvable examples are presented.