# Carroll symmetry of plane gravitational waves

## TL;DR

This paper reveals that the symmetry group of plane gravitational waves aligns with the Carroll group in 2+1 dimensions, linking gravitational wave geometry to Carrollian structures and exploring light scattering properties.

## Contribution

It establishes a connection between plane gravitational wave symmetries and Carroll groups, providing new geometric insights and analyzing light scattering as a metamaterial.

## Key findings

- Plane waves' isometry group is identified as the Carroll group.
- Plane waves can be embedded into Bargmann spaces, linking to Carroll manifolds.
- Calculated electric permittivity of gravitational waves as metamaterials.

## Abstract

The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.