Geodesic motion in Bogoslovsky-Finsler Spacetimes
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arXiv
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| Format: | Preprint |
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2020
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| author | Elbistan, M. Zhang, P. -M. Dimakis, N. Gibbons, G. W. Horvathy, P. A. |
| author_facet | Elbistan, M. Zhang, P. -M. Dimakis, N. Gibbons, G. W. Horvathy, P. A. |
| contents | We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_02751 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Geodesic motion in Bogoslovsky-Finsler Spacetimes Elbistan, M. Zhang, P. -M. Dimakis, N. Gibbons, G. W. Horvathy, P. A. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model. |
| title | Geodesic motion in Bogoslovsky-Finsler Spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2004.02751 |