Kerr geodesics in terms of Weierstrass elliptic functions

authored by

Adam Cieślik, Eva Hackmann, Patryk Mach

Abstract

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parametrized 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.

External Organisation(s)

Jagiellonian University
Center of Applied Space Technology and Microgravity (ZARM)

Type

Article

Journal

Physical Review D

Volume

108

ISSN

2470-0010

Publication date

24.07.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics

Electronic version(s)

https://doi.org/10.1103/PhysRevD.108.024056 (Access: Unknown)