A novel approach to the dynamics of Szekeres dust models

Abstract

Abstract. We obtain an elegant and useful description of the dynamics of Szekeres dust models (in their full generality) by means of "quasi-local" scalar variables constructed by suitable integral distributions that can be interpreted as weighed proper volume averages of the local covariant scalars. In terms of these variables, the field equations and basic physical and geometric quantities are formally identical to their corresponding expressions in the spherically symmetric LTB dust models. Since we can map every Szekeres model to a unique LTB model, rigorous results valid for the latter models can be readily generalized to a nonspherical Szekeres geometry. The new variables lead naturally to an initial value formulation in which all scalars are expressed as scaling laws in terms of their values at an arbitrary initial space slice. These variables also yield a significant simplification of numerical work, since the fluid flow evolution equations become a system of autonomous ordinary differential equations subjected to algebraic constraints containing the information on the deviations from spherical symmetry. As an example of how this formalism can be applied, we show that spherical symmetry is stable against small dipole-like perturbations. This new approach to the dynamics of the Szekeres solutions has an enormous potential for dealing with a wide variety of theoretical issues and for constructing non-spherical models of cosmological inhomogeneities to fit observational data.

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis

“…In fact, it is straightforward to generalise LTB models to non-spherical Szekeres models, which are endowed with more degrees of freedom and thus allow for a fully relativistic description and modelling of multiple structures [50][51][52]. We are currently undertaking further efforts to extend the present work to probe non-linear observational effects of theoretical assumptions on CDM and DE sources.…”

Scalar averaging in Szekeres dust models

“…They are also valuable tools to study open theoretical issues, such as the averaging problem in General Relativity. A convenient description of these models is furnished by the metric element [2] …”

“…where R = R(t, r) and Y = ∂Y /∂ r, while the free functions K, S, P, Q depend only on r. As shown in [2], the usage of the metric variables (1) allows for a direct generalization to the non-spherical Szekeres models of most formal results derived for the spherical LTB models. For example, the field equations reduce to forms that are very similar to those of LTB models:…”

“…An alternative way of looking at the dynamics of the models is through the fluid flow evolution equations for the covariant scalars {ρ, H , Σ, W } (see [2]):ρ…”

Vorticity and entropy production in tilted Szekeres spacetimes

“…Physical and topological properties of Szekeres spacetimes, as well as the problem of structure formation and other cosmological related issues have been considered in [25][26][27][28][29][30][31][32][33][34].…”