A Newtonian analogue of Kerr black hole

Abstract

A 250-year old Newtonian problem, first studied by Euler, turns out to share a lot of similarities with the most extreme astrophysical relativistic object, the Kerr black hole. Although the framework behind the two fields is completely different, both problems are related to gravitational fields that have quite intriguing analogies with respect to orbital motions of a test-body in them. The fundamental reason responsible for their extraordinary similarity is the integrability of both problems, as well as their common multipolar structure. In this paper we demonstrate the existence of a multitude of either qualitative, and sometimes quantitative, similarities between the two problems. Based on this analogy, one could use the Newtonian problem to get insight in cases where the relativistic treatment of the field of a Kerr black hole becomes quite complicated.

64 pages, 13 figures

References in corpus (3)

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Importance of transient resonances in extreme-mass-ratio inspirals
• Carter-like constants of the motion in Newtonian gravity and electrodynamics

Cited by in corpus (7)

• Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals
• Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle-Thorne spacetime
• Non-linear effects in EMRI dynamics and their imprints on gravitational waves
• Testing gravity with Extreme-Mass-Ratio Inspirals
• Nonlocal modification of the Kerr metric
• Tidally-induced nonlinear resonances in EMRIs with an analogue model
• Chaotic particle motion around a homogeneous circular ring