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.

15 pages, 3 figures. To appear in Class. Quant. Grav

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• Flat Holography: Aspects of the dual field theory
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• Non-Lorentzian Field Theories with Maximal Supersymmetry and Moduli Space Dynamics
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• Quantization of Carrollian conformal scalar theories
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• Towards Carrollian quantization: renormalization of Carrollian electrodynamics
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• The memory effect in impulsive plane waves: comments, corrections, clarifications
• Memory Effect and Carroll Symmetry: 50 years later
• On Integrability of the Geodesic Deviation Equation
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• Sengupta Transformations and Carrollian Relativistic Theory
• A New Twist on the Geometry of Gravitational Plane Waves
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