Gravitational Waves and Conformal Time Transformations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866913842801410048 |
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| author | Zhang, P. -M. Zhao, Q. -L. Horvathy, P. A. |
| author_facet | Zhang, P. -M. Zhao, Q. -L. Horvathy, P. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09589 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Gravitational Waves and Conformal Time Transformations Zhang, P. -M. Zhao, Q. -L. Horvathy, P. A. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 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. |
| title | Gravitational Waves and Conformal Time Transformations |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2112.09589 |