Details
| Original language | English |
|---|---|
| Article number | 024056 |
| Journal | Physical Review D |
| Volume | 108 |
| Issue number | 2 |
| Publication status | Published - 24 Jul 2023 |
| Externally published | Yes |
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 subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Physical Review D, Vol. 108, No. 2, 024056, 24.07.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Kerr geodesics in terms of Weierstrass elliptic functions
AU - Cieślik, Adam
AU - Hackmann, Eva
AU - Mach, Patryk
N1 - Publisher Copyright: © 2023 American Physical Society.
PY - 2023/7/24
Y1 - 2023/7/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85166772526&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.108.024056
DO - 10.1103/PhysRevD.108.024056
M3 - Article
AN - SCOPUS:85166772526
VL - 108
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 2
M1 - 024056
ER -