The Orbital Lense-Thirring Precession in a Strong Field

• Published in: arXiv.org 2019-06
• Main Authors: Strokov, Vladimir N, Khlghatyan, Shant
• Format: Article
• Language: English
• Subjects: Angular momentum; Deviation; Gravitational fields; Hodographs; Nutation; Orbits; Parameters; Precession
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1906.05309

We study the exact evolution of the orbital angular momentum of a massive particle in the gravitational field of a Kerr black hole. We show analytically that, for a wide class of orbits, the angular momentum's hodograph is always close to a circle. This applies to both bounded and unbounded orbits that do not end up in the black hole. Deviations from the circular shape do not exceed \(\approx10\%\) and \(\approx7\%\) for bounded and unbounded orbits, respectively. We also find that nutation provides an accurate approximation for those deviations, which fits the exact curve within \(\sim 0.01\%\) for the orbits of maximal deviation. Remarkably, the more the deviation, the better the nutation approximates it. Thus, we demonstrate that the orbital Lense-Thirring precession, originally obtained in the weak-field limit, is also a valid description in the general case of (almost) arbitrary exact orbits. As a by-product, we also derive the parameters of unstable spherical timelike orbits as a function of their radii and arbitrary rotation parameter \(a\) and Carter's constant \(Q\). We verify our results numerically for all the kinds of orbits studied.