"Kepler Harmonies" and conformal symmetries

Abstract

Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to $5$-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.

Affiliation corrected

References in corpus (13)

• Monitoring stellar orbits around the Massive Black Hole in the Galactic Center
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Non-relativistic conformal symmetries in fluid mechanics
• Indication of Another Intermediate-mass Black Hole in the Galactic Center
• Symmetries of fluid dynamics with polytropic exponent
• Discrete Newtonian Cosmology
• Scaling and conformal symmetries for plane gravitational waves
• Memory effect, conformal symmetry and gravitational plane waves
• A generalized Noether theorem for scaling symmetry
• Discrete Newtonian Cosmology: Perturbations
• Null lifts and projective dynamics
• On the Schr{ö}dinger-Newton equation and its symmetries: a geometric view
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Cited by in corpus (6)

• Scaling and conformal symmetries for plane gravitational waves
• A generalized Noether theorem for scaling symmetry
• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
• Integrability of geodesic motions in curved manifolds through non-local conserved charges
• Hidden symmetries from distortions of the conformal structure
• Displacement Memory Effect from Supersymmetry