Kerr geodesics in terms of Weierstrass elliptic functions

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Adam Cieślik
  • Eva Hackmann
  • Patryk Mach

Externe Organisationen

  • Jagiellonian University
  • Zentrum für angewandte Raumfahrt­technologie und Mikro­gravitation (ZARM)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer024056
FachzeitschriftPhysical Review D
Jahrgang108
Ausgabenummer2
PublikationsstatusVeröffentlicht - 24 Juli 2023
Extern publiziertJa

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.

ASJC Scopus Sachgebiete

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Kerr geodesics in terms of Weierstrass elliptic functions. / Cieślik, Adam; Hackmann, Eva; Mach, Patryk.
in: Physical Review D, Jahrgang 108, Nr. 2, 024056, 24.07.2023.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Cieślik A, Hackmann E, Mach P. Kerr geodesics in terms of Weierstrass elliptic functions. Physical Review D. 2023 Jul 24;108(2):024056. doi: 10.1103/PhysRevD.108.024056
Cieślik, Adam ; Hackmann, Eva ; Mach, Patryk. / Kerr geodesics in terms of Weierstrass elliptic functions. in: Physical Review D. 2023 ; Jahrgang 108, Nr. 2.
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