The well-known 5-parameter isometry group of plane gravitational waves in 4 dimensions is identified as Lévy-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.
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