Generalized Carter constant for quadrupolar test bodies in Kerr spacetime

Compère, Geoffrey; Druart, Adrien; Vines, Justin

doi:10.48550/arxiv.2302.14549

Cited by 1 publication

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“…The study of Kerr geodesics began since the Kerr solution was discovered in 1963 [14]. In 1968, Carter found an extra conserved quantity called the Carter constant [15] during the geodesic motion in Kerr spacetime, which was further discussed in [16]. Wilkins [17] studied the bound geodesics in Kerr spacetime.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions of equatorial geodesic motion in Kerr spacetime*

Liu 刘,

Sun 孙

2024

Chinese Phys. C

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The study of Kerr geodesics has a long history, particularly for those occurring within the equatorial plane, which is generally well-understood. However, upon comparison with the classification introduced by one of us \href{https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.024075}{[Phys. Rev. D 105, 024075 (2022)]}, it becomes apparent that certain classes of geodesics, such as trapped orbits, are still lacking analytical solutions. Thus, in this study, we provide explicit analytical solutions for equatorial timelike geodesics in Kerr spacetime, including solutions of trapped orbits, which capture the characteristics of special geodesics, such as the positions and conserved quantities of circular orbits, bound orbits, and deflecting orbits. Specifically, we determine the precise location at which retrograde orbits undergo a transition from counter-rotating to prograde motion due to the strong gravitational effects near the rotating black hole. Interestingly, we observe that for orbits with negative energy, the trajectory remains prograde despite the negative angular momentum. Furthermore, we investigate the intriguing phenomenon of deflecting orbits exhibiting an increased number of revolutions around the black hole as the turning point approaches the turning point of the trapped orbit. Additionally, we find that only prograde marginal deflecting geodesics are capable of traversing through the ergoregion. In summary, our findings present explicit solutions for equatorial timelike geodesics and offer insights into the dynamics of particle motion in the vicinity of a rotating black hole.

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