The separable analogue of Kerr in Newtonian gravity

TL;DR

This paper identifies Euler's two-fixed centers problem as the unique Newtonian potential that exhibits the same separability properties as the Kerr metric in General Relativity, linking classical and relativistic gravitational symmetries.

Contribution

It demonstrates that Euler's two-fixed centers problem uniquely mirrors Kerr's separability features in Newtonian gravity.

Findings

Euler's two-fixed centers problem is the Newtonian analogue of Kerr's separability.

This potential allows for separable equations for both particle and wave motion.

The result bridges classical Newtonian and relativistic gravitational symmetries.

Abstract

General Relativity's Kerr metric is famous for its many symmetries which are responsible for the separability of the Hamilton-Jacobi equation governing the geodesic motion and of the Teukolsky equation for wave dynamics. We show that there is a unique stationary and axisymmetric Newtonian gravitational potential that has exactly the same dual property of separable point-particle and wave motion equations. This `Kerr metric analogue' of Newtonian gravity is none other than Euler's 18th century problem of two-fixed gravitating centers.