Scaling and conformal symmetries for plane gravitational waves

Understand

The isometries of an exact plane gravitational wave are symmetries for both massive and massless particles.

• Their conformal extensions are in fact chrono-projective transformations introduced earlier by Duval et al are symmetries for massless particles.
• Homotheties are universal chrono-projective symmetries for any profile.
• Chrono-projective transformations also generate new conserved quantities for the underlying non-relativistic systems in the Bargmann framework.