Carroll symmetry of plane gravitational waves

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.
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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. ⟨http://stacks.iop.org/0264-9381/34/i=17/a=175003⟩. ⟨hal-01504485⟩

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