Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity

TL;DR

This paper studies the long-term behavior and stability of solutions in a relativistic gravitational model, demonstrating dispersion estimates and stability of certain static solutions using variational methods.

Contribution

It establishes the asymptotic dispersion and orbital stability of steady states in the Nordström-Vlasov system, a relativistic extension of classical gravitational models.

Findings

Solutions with energy ≥ mass satisfy dispersion estimates.

Existence and stability of isotropic polytropes under perturbations.

Orbital stability proven via variational energy minimization.

Abstract

The Nordstr\"om-Vlasov system is a relativistic Lorentz invariant generalization of the Vlasov-Poisson system in the gravitational case. The asymptotic behavior of solutions and the non-linear stability of steady states are investigated. It is shown that solutions of the Nordstr\"om-Vlasov system with energy grater or equal to the mass satisfy a dispersion estimate in terms of the conformal energy. When the energy is smaller than the mass, we prove existence and non-linear (orbital) stability of a class of static solutions (isotropic polytropes) against general perturbations. The proof of orbital stability is based on a variational problem associated to the minimization of the energy functional under suitable constraints.