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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
CPT - Centre de Physique Théorique - UMR 7332
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
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.
Keywords : scattering of light Plane gravitational waves Carroll group
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  • ARXIV : 1702.08284

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

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