A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

TL;DR

This paper introduces a non-variational method to establish the nonlinear stability of the King model in stellar dynamics, overcoming limitations of previous variational approaches and providing new insights into astrophysical equilibrium states.

Contribution

The paper presents a novel non-variational approach to prove nonlinear stability of the King model, expanding analytical tools in stellar dynamics.

Findings

Proves nonlinear stability of the King model.

Demonstrates effectiveness of non-variational techniques.

Addresses a class of spherically symmetric perturbations.

Abstract

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques.