Carroll symmetry of plane gravitational waves

Christian Duval (1, 2) , G. W. Gibbons (3, 4) , P. A. Horvathy (4, 5) , P. -M. Zhang (5)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E2 Géométrie, Physique et Symétries
3 DAMTP - Department of Applied Mathematics and Theoretical Physics
4 LMPT - Laboratoire de Mathématiques et Physique Théorique
5 IMP - Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

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.

Mots clés: scattering of light; Plane gravitational waves; Carroll group

Domaines: Physique mathématique [math-ph]

Christian Duval, G. W. Gibbons, P. A. Horvathy, P. -M. Zhang. Carroll symmetry of plane gravitational waves. Classical and Quantum Gravity, 2017, 34 (17), pp.175003. ⟨hal-01504485⟩