Kerr Geodesics in Terms of Weierstrass Elliptic Functions
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| Autori principali: | , , |
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| Natura: | Dataset Open Access |
| Lingua: | en |
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PANGAEA
2023
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| _version_ | 1867171885629833216 |
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| author | Cieślik, Adam Hackmann, Eva Mach, Patryk |
| author_facet | Cieślik, Adam Hackmann, Eva Mach, Patryk |
| collection | Datos científicos de ciencias marinas y ambientales |
| contents | We provide a code package written in Wolfram Mathematica to calculate the motion of test particles around a Kerr black hole. The novel analytical solutions describe both timelike and null geodesics. They are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial and polar type. This uniformity has been achieved by applying a little-known result due to Biermann and Weierstrass, regarding solutions of a certain class of ordinary differential equations. Different from other expressions in terms of Weierstrass functions, our solution is explicitly real for all types of geodesics. In particular, for the first time the so-called transit orbits are now expressed by explicitly real Weierstrass functions. In addition to the code package itself a description and demonstration file is also available. |
| format | Dataset Open Access |
| id | pangaea_https___doi_org_10_1594_PANGAEA_960855 |
| institution | PANGAEA |
| language | en |
| publishDate | 2023 |
| publisher | PANGAEA |
| record_format | pangaea |
| spellingShingle | Kerr Geodesics in Terms of Weierstrass Elliptic Functions Cieślik, Adam Hackmann, Eva Mach, Patryk analytic methods; Binary Object; Binary Object (File Size); Description; File format; File name; Kerr geodesic; Title; Weierstrass elliptic functions We provide a code package written in Wolfram Mathematica to calculate the motion of test particles around a Kerr black hole. The novel analytical solutions describe both timelike and null geodesics. They are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial and polar type. This uniformity has been achieved by applying a little-known result due to Biermann and Weierstrass, regarding solutions of a certain class of ordinary differential equations. Different from other expressions in terms of Weierstrass functions, our solution is explicitly real for all types of geodesics. In particular, for the first time the so-called transit orbits are now expressed by explicitly real Weierstrass functions. In addition to the code package itself a description and demonstration file is also available. |
| title | Kerr Geodesics in Terms of Weierstrass Elliptic Functions |
| topic | analytic methods; Binary Object; Binary Object (File Size); Description; File format; File name; Kerr geodesic; Title; Weierstrass elliptic functions |
| url | https://doi.org/10.1594/PANGAEA.960855 |