A Newtonian analogue of Kerr black hole

TL;DR

This paper explores a Newtonian problem related to Euler's work that shares remarkable similarities with Kerr black holes, providing insights into complex relativistic phenomena through a simpler Newtonian analogue.

Contribution

It demonstrates a detailed analogy between a classical Newtonian problem and Kerr black holes, highlighting their shared integrability and multipolar structure.

Findings

Multiple qualitative similarities identified between Newtonian problem and Kerr black holes

Quantitative parallels in orbital motion behaviors

Potential for using Newtonian models to understand complex relativistic fields

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.