Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics

TL;DR

This paper establishes a new local condition on the distribution function that guarantees finite mass and compact support of spherically symmetric equilibrium states in both non-relativistic and relativistic galactic dynamics models.

Contribution

It introduces a novel local condition on the distribution function ensuring finite mass and compact support in stationary solutions for Vlasov-Poisson and Vlasov-Einstein systems.

Findings

Guarantees finite mass and compact support for equilibrium states.

Applicable to both non-relativistic and relativistic models.

Condition depends only on asymptotic behavior near maximal energy.

Abstract

Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically symmetric stationary solutions the distribution function of the particles (stars) on phase space is taken to be a function of the particle energy and angular momentum. We give a new condition on this function which guarantees that the resulting steady state has finite mass and compact support both for the non-relativistic and the relativistic case. The condition is local in the sense that only the asymptotic behaviour for energy values close to the maximal energy value in the particle distribution needs to be prescribed.