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“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.
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Submitted on : Wednesday, March 20, 2019 - 12:46:09 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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P.-M. Zhang, M. Cariglia, M. Elbistan, G.W. Gibbons, P.A. Horvathy. “Kepler Harmonies” and conformal symmetries. Physics Letters B, Elsevier, 2019, 792, pp.324-328. ⟨10.1016/j.physletb.2019.03.057⟩. ⟨hal-02073484⟩

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