Relative equilibria in continuous stellar dynamics

TL;DR

This paper investigates a 3D continuous gravitating system rotating at constant angular velocity, proving the existence of complex stationary solutions that resemble multiple point particles, linking continuous models with N-body dynamics.

Contribution

It introduces a finite dimensional reduction method to establish the existence of non-radial stationary solutions with multiple disjoint supports in a rotating continuous stellar model.

Findings

Existence of non-radial stationary solutions with multiple supports.

Solutions behave like point particles at first order.

Link established between continuous models and N-body relative equilibria.

Abstract

We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose supports are made of an arbitrarily large number of disjoint compact sets, in the low angular velocity and large scale limit. At first order, the solutions behave like point particles, thus making the link with the relative equilibria} in N-body dynamics.