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.
https://hal.archives-ouvertes.fr/hal-01504485 Contributor : Christian DuvalConnect in order to contact the contributor Submitted on : Wednesday, April 25, 2018 - 3:22:34 PM Last modification on : Tuesday, January 11, 2022 - 5:56:10 PM Long-term archiving on: : Tuesday, September 25, 2018 - 4:17:14 AM
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⟩