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arXiv · 2112.09589

Gravitational Waves and Conformal Time Transformations

P. -M. Zhang·Q. -L. Zhao·P. A. Horvathy
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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.

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P. -M. Zhang, Q. -L. Zhao, P. A. Horvathy. 2021-12-17. Gravitational Waves and Conformal Time Transformations. https://doi.org/10.1016/j.aop.2022.168833

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