Equilibrium configurations in the dynamics of irrotational dust matter

TL;DR

This paper analyzes the equilibrium states of irrotational dust solutions in Einstein's equations, providing a covariant framework to understand their role in cosmic structure formation.

Contribution

It offers a comprehensive state space analysis of irrotational dust models, characterizing equilibrium configurations and initial data for diverse inhomogeneous and homogeneous cases.

Findings

Equilibrium configurations correspond to invariant sets in the dynamics.

Characterization of initial data for various dust models.

Framework applicable to highly inhomogeneous cosmological models.

Abstract

Irrotational dust solutions of Einstein's equations are suitable models to describe the general-relativistic aspects of the gravitational instability mechanism for the formation of cosmic structures. In this paper we study their state space by considering the local initial-value problem formulated in the covariant fluid approach. We consider a wide range of models, from homogeneous and isotropic to highly inhomogeneous irrotational dust models, showing how they constitute equilibrium configurations (invariant sets) of the dynamics. Moreover, we give the characterization of such configurations, which provides an initial-data characterization of the models under consideration.