Self-gravitating stationary spherically symmetric systems in relativistic galactic dynamics

TL;DR

This paper analyzes equilibrium states in relativistic galactic dynamics using the Einstein-Vlasov system, deriving conditions for finite radii and masses through dynamical systems analysis.

Contribution

It introduces a new dynamical systems approach to study relativistic steady states, establishing theorems ensuring finite size and mass of solutions.

Findings

Steady state solutions have finite radii and masses.

Reformulation of Einstein-Vlasov equations into a 3D autonomous system.

New theorems guarantee finite extent and mass of equilibrium states.

Abstract

We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a bounded state space. Based on a dynamical systems analysis we derive new theorems that guarantee that the steady state solutions have finite radii and masses.