Gravitational Waves and Conformal Time Transformations
Abstract
Recent interest in the "memory effect" prompted us to revisit the relation of gravitational aves and oscillators. 50 years ago Niederer [1] found that an isotropic harmonic oscillator with a constant frequency can be mapped onto a free particle. Later Takagi [2] has shown that "time-dependent scaling" extends the oscillator versus free particle correspondence to a time-dependent frequency when the scale factor satisfies a Sturm-Liouville equation. More recently Gibbons [3] pointed out that time redefinition is conveniently studied in terms of the Schwarzian derivative. The oscillator versus free particle correspondence "Eisenhart-Duval lifts" to a conformal transformation between Bargmann spaces [4-7]. These methods are extended to spacetimes which are not conformally flat and have a time-dependent profile, and can then be applied to the geodesic motion in a plane gravitational wave.
Cite
@article{arxiv.2112.09589,
title = {Gravitational Waves and Conformal Time Transformations},
author = {P. -M. Zhang and Q. -L. Zhao and P. A. Horvathy},
journal= {arXiv preprint arXiv:2112.09589},
year = {2025}
}
Comments
affiliation corrected