Modelling Inhomogeneity in Szekeres Spacetime

Abstract

We study the behaviour of the density contrast in quasi-spherical Szekeres spacetime and derive its analytical behaviour as a function of $t$ and $r$. We set up the inhomogeneity using initial data in the form of one extreme value of the density and the radial profile. We derive conditions for density extremes that are necessary for avoiding the shell crossing singularity and show that in the special case of a trivial curvature function, the conditions are preserved by evolution. We also show that in this special case if the initial inhomogeneity is small, the time evolution does not influence the density contrast, however its magnitude homogeneously decreases.

arXiv comment7 figures

References in corpus (15)

• Szekeres Swiss-Cheese model and supernova observations
• The Szekeres Swiss Cheese model and the CMB observations
• You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models
• Formation of a galaxy with a central black hole in the Lemaitre-Tolman model
• Structure formation in the quasispherical Szekeres model
• Evolution of cosmic structures in different environments in the quasispherical Szekeres model
• A novel approach to the dynamics of Szekeres dust models
• Formation of voids in the Universe within the Lemaitre-Tolman model
• More examples of structure formation in the Lemaitre-Tolman model
• Alternative Methods of Describing Structure Formation in the Lemaitre-Tolman Model
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Geometry and topology of the quasi-plane Szekeres model
• Volume averaging in the quasispherical Szekeres model
• Constructing Realistic Szekeres Models from Initial and Final Data
• Geometry of the quasi-hyperbolic Szekeres models

Cited by in corpus (12)

• Multiple non-spherical structures from the extrema of Szekeres scalars
• Coarse-grained description of cosmic structure from Szekeres models
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Symmetry and Equivalence in Szekeres Models
• Quantization of the Szekeres System
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Frame Rotation in the Szekeres Spacetimes
• Inhomogeneous spacetimes in Einstein-æther Cosmology
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Quantum potentiality in Inhomogeneous Cosmology
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Quasilocal horizons in inhomogeneous cosmological models