Related papers: Szekeres models: a covariant approach
The exact Friedman solution to the field equations of General Relativity (GR) describing a homogeneous and isotropic universe together with its linear and higher-order perturbations are the theoretical roots of the current standard model of…
We examine the spatial extrema (local maxima, minima and saddle points) of the covariant scalars (density, Hubble expansion, spatial curvature and eigenvalues of the shear and electric Weyl tensors) of the quasi-spherical Szekeres dust…
We study the occurrence and nature of naked singularities for a dust model with non-zero cosmological constant in ($n+2$)-dimensional Szekeres space-times (which possess no Killing vectors) for $n\geq 2$. We find that central shell-focusing…
We show that the canonical formulation of a generic action for 1+1-dimensional models of gravity coupled to matter admits a description in terms of Ashtekar-type variables. This includes the CGHS model and spherically symmetric reductions…
The cosmological tensions present in the $\Lambda$ cold dark matter model that have emerged and strengthened over recent years motivate model independent approaches to analysing data. Cosmography is useful for interpreting data in cosmology…
Inhomogeneous cosmological models are able to fit cosmological observations without dark energy under the assumption that we live close to the "center" of a very large-scale under-dense region. Most studies fitting observations by means of…
A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant,…
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational…
We present the exact equations governing the dynamics of a spherically-symmetric inhomogeneous model with n decoupled and non-comoving perfect fluids. Thanks to the use of physically meaningful quantities we write the set of 3+2n equations…
We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a…
We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3--dimensional networks of cold dark matter structures (over--densities and/or density voids) undergoing "pancake" collapse.…
The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain a…
The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the…
We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows…
The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Here we present a model construction procedure for the quasispherical…
The notion of an apparent horizon (AH) in a collapsing object can be carried over from the Lema\^{\i}tre -- Tolman (L--T) to the quasispherical Szekeres models in three ways: 1. Literally by the definition -- the AH is the boundary of the…
We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $p_{g}=\left( \gamma-1\right) \rho_{g},$ where $\gamma$ is a constant. The field equations…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
We study the properties and behaviour of the quasi-pseudospherical and quasi-planar Szekeres models, obtain the regularity conditions, and analyse their consequences. The quantities associated with "radius" and "mass" in the quasi-spherical…
We want to establish the basic properties of a scale invariant cosmology, that also accounts for the hypothesis of scale invariance of the empty space at large scales. We write the basic analytical properties of the scale invariant…