Kerr Geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929554822529024 |
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| author | Bakun, Zuzanna Łukanty, Angelika Untilova, Anastasiia Cieślik, Adam Mach, Patryk |
| author_facet | Bakun, Zuzanna Łukanty, Angelika Untilova, Anastasiia Cieślik, Adam Mach, Patryk |
| contents | We revisit the theory of timelike and null geodesics in the (extended) Kerr spacetime. This work is a sequel to a recent paper by Cieślik, Hackmann, and Mach, who applied the so-called Biermann-Weierstrass formula to integrate Kerr geodesic equations expressed in Boyer-Lindquist coordinates. We show that a formulation based on the Biermann-Weierstrass theorem can also be applied in horizon-penetrating Kerr coordinates, resulting in solutions that are smooth across Kerr horizons. Horizon-penetrating Kerr coordinates allow for an explicit continuation of timelike and null geodesics between appropriate regions of the maximal analytic extension of the Kerr spacetime. A part of this work is devoted to a graphic visualisation of such geodesics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kerr Geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions Bakun, Zuzanna Łukanty, Angelika Untilova, Anastasiia Cieślik, Adam Mach, Patryk General Relativity and Quantum Cosmology We revisit the theory of timelike and null geodesics in the (extended) Kerr spacetime. This work is a sequel to a recent paper by Cieślik, Hackmann, and Mach, who applied the so-called Biermann-Weierstrass formula to integrate Kerr geodesic equations expressed in Boyer-Lindquist coordinates. We show that a formulation based on the Biermann-Weierstrass theorem can also be applied in horizon-penetrating Kerr coordinates, resulting in solutions that are smooth across Kerr horizons. Horizon-penetrating Kerr coordinates allow for an explicit continuation of timelike and null geodesics between appropriate regions of the maximal analytic extension of the Kerr spacetime. A part of this work is devoted to a graphic visualisation of such geodesics. |
| title | Kerr Geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2409.03722 |