Kerr Geodesics in Terms of Weierstrass Elliptic Functions

DOI

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.

Identifier
DOI https://doi.org/10.1594/PANGAEA.960855
Related Identifier References https://doi.org/10.48550/arXiv.2305.07771
Metadata Access https://ws.pangaea.de/oai/provider?verb=GetRecord&metadataPrefix=datacite4&identifier=oai:pangaea.de:doi:10.1594/PANGAEA.960855
Provenance
Creator Cieślik, Adam; Hackmann, Eva; Mach, Patryk
Publisher PANGAEA
Publication Year 2023
Rights Creative Commons Attribution 4.0 International; https://creativecommons.org/licenses/by/4.0/
OpenAccess true
Representation
Resource Type Dataset
Format text/tab-separated-values
Size 15 data points
Discipline Earth System Research