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Free keywords:
General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
Abstract:
We present closed-form solutions for plunging geodesics in the extended Kerr
spacetime using Boyer-Lindquist coordinates. Our solutions directly solve for
the dynamics of generic timelike plunges, we also specialise to the case of
test particles plunging from a precessing innermost stable circular orbit
(ISSO). We find these solutions in the form of elementary and Jacobi elliptic
functions parameterized by Mino time. In particular, we demonstrate that
solutions for the ISSO case can be determined almost entirely in terms of
elementary functions, depending only on the spin parameter of the black hole
and the radius of the ISSO. This extends recent work on the case of equatorial
plunges from the innermost stable circular orbit. Furthermore, we introduce a
new equation that characterizes the radial inflow from the ISSO to the horizon,
taking into account the inclination. For ease of application, our results have
been implemented in the KerrGeodesics package in the Black Hole Perturbation
Toolkit.
