Kerr-fully Diving into the Abyss: Analytic Solutions to Plunging Geodesics in Kerr
Conor Dyson, Maarten van de Meent

TL;DR
This paper derives explicit analytical solutions for plunging geodesics in Kerr spacetime, including special cases from the ISSO, and provides practical tools for black hole physics research.
Contribution
It introduces closed-form solutions for generic and ISSO plunging geodesics in Kerr spacetime, extending previous work and implementing these in a computational toolkit.
Findings
Solutions expressed in elementary and elliptic functions
Almost elementary solutions for ISSO plunges depending only on spin and radius
New equation for radial inflow from ISSO to horizon including inclination
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…
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Taxonomy
TopicsAstrophysical Phenomena and Observations · Pulsars and Gravitational Waves Research · Black Holes and Theoretical Physics
