Dynamical system describing cloud of particles in relativistic and non-relativistic framework

TL;DR

This paper develops a dynamical system framework for self-gravitating particles, proving the existence of heteroclinic trajectories and deriving critical mass-radius bounds in both relativistic and non-relativistic astrophysical models.

Contribution

It introduces a general class of dynamical systems with Lyapunov functions and proves heteroclinic trajectory existence, leading to a critical mass-radius theorem for astrophysical models.

Findings

Existence of heteroclinic trajectories in the models

Upper bounds for trajectories related to critical mass-radius

Application to both relativistic and non-relativistic frameworks

Abstract

We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by integrated densities approach to some astrophysical models of self-gravitating particles both in relativistic and non--relativistic frameworks. Finally, with the aid of geometric and topological reasoning we find the upper bounds for this trajectory yielding the critical mass--radius theorem for the astrophysical model.