# Description of the evolution of inhomogeneities on a Dark Matter halo with the Vlasov equation

## TL;DR

This paper numerically investigates how inhomogeneities in dark matter halos evolve over time using the Vlasov equation, revealing model-dependent signatures in their stationary states.

## Contribution

It introduces a numerical approach to study the evolution of dark matter inhomogeneities with the Vlasov equation in spherical symmetry, highlighting model-specific signatures.

## Key findings

- Identification of distinctive stationary states for different halo models
- Demonstration of the evolution process of inhomogeneities in dark matter halos
- Characterization of features associated with virialization in the system

## Abstract

We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo. Such a collection is assumed to represent a dark matter inhomogeneity which reaches a stationary state determined by the virialization of the system. We describe some features of the stationary states and, by using several halo models, obtain distinctive signatures for the evolution of the inhomogeneities in each of the models.