The Orbital Lense-Thirring Precession in a Strong Field. (arXiv:1906.05309v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Strokov_V/0/1/0/all/0/1">Vladimir N. Strokov</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Khlghatyan_S/0/1/0/all/0/1">Shant Khlghatyan</a>
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.
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.
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