# Celestial mechanics, conformal structures, and gravitational waves.

@article{Duval1991CelestialMC, title={Celestial mechanics, conformal structures, and gravitational waves.}, author={Duval and Gibbons and Horv{\'a}thy}, journal={Physical review. D, Particles and fields}, year={1991}, volume={43 12}, pages={ 3907-3922 } }

Newton's equations for the motion of $N$ nonrelativistic point particles attracting according to the inverse square law may be cast in the form of equations for null geodesics in a ($3N+2$)-dimensional Lorentzian spacetime which is Ricci flat and admits a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a plane-fronted gravitational wave (generalized pp wave). Bargmann electromagnetism in five dimensions actually comprises the two…

## 335 Citations

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