Spherically symmetric Einstein-aether perfect fluid models

TL;DR

This paper explores the dynamics of spherically symmetric Einstein-aether cosmological models with perfect fluids, analyzing stability, asymptotic behavior, and static solutions using a well-structured formalism suitable for numerical and qualitative studies.

Contribution

It introduces a comprehensive 1+3 formalism with normalized variables for Einstein-aether models, enabling detailed stability and asymptotic analyses of inhomogeneous cosmologies.

Findings

Stable equilibrium points identified for realistic parameter values.

Derived reduced evolution system for dust models.

Analyzed future asymptotic behavior of Kantowski-Sachs models.

Abstract

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in ($\beta-$) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.