A novel approach to the dynamics of Szekeres dust models

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 non-spherical 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.

26 pages, 2 figures

References in corpus (46)

• Unified first law of black-hole dynamics and relativistic thermodynamics
• Gravitational Energy in Spherical Symmetry
• An inhomogeneous alternative to dark energy?
• General Relativistic Dynamics of Irrotational Dust: Cosmological Implications
• Lemaitre-Tolman-Bondi model and accelerating expansion
• Inhomogeneous cosmological models: exact solutions and their applications
• Effect of inhomogeneities on the expansion rate of the Universe
• On cosmological observables in a swiss-cheese universe
• The effect of inhomogeneous expansion on the supernova observations
• CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe
• Light-cone averages in a swiss-cheese universe
• Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes
• The supernova Hubble diagram for off-center observers in a spherically symmetric inhomogeneous universe
• Integrability of irrotational silent cosmological models
• Szekeres Swiss-Cheese model and supernova observations
• The Possibility of Cosmic Acceleration via Spatial Averaging in Lemaitre-Tolman-Bondi Models
• Dynamics of Silent Universes
• Long wavelength iteration of Einstein's equations near a spacetime singularity
• 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
• A Local View of the Observable Universe
• Structure formation in the quasispherical Szekeres model
• Evolution of cosmic structures in different environments in the quasispherical Szekeres model
• Quasi-local variables in spherical symmetry: numerical applications to dark matter and dark energy sources
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
• Back-reaction and effective acceleration in generic LTB dust models
• Inhomogeneity-Induced Cosmic Acceleration in a Dust Universe
• Redshift and distances in a ΛCDM cosmology with non-linear inhomogeneities
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• Supernovae Ia observations in the Lemaitre--Tolman model
• The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models
• Geometry and topology of the quasi-plane Szekeres model
• Volume averaging in the quasispherical Szekeres model
• Radial asymptotics of Lemaitre-Tolman-Bondi dust models
• A dynamical system approach to inhomogeneous dust solutions
• Regular spherical dust spacetimes
• Matching Spherical Dust Solutions to Construct Cosmological Models
• On spatial volume averaging in Lema\^ıtre--Tolman--Bondi dust models. Part I: back reaction, spacial curvature and binding energy
• Nonperturbative gravito-magnetic fields
• Covariant Fluid Dynamics: a Long Wave-Length Approximation
• Quasi-local variables and scalar averaging in LTB dust models
• A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models

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• Hubble flow variance and the cosmic rest frame
• Back-reaction and effective acceleration in generic LTB dust models
• Relativistic numerical cosmology with Silent Universes
• Identification of black hole horizons using scalar curvature invariants
• Multiple non-spherical structures from the extrema of Szekeres scalars
• Vorticity and entropy production in tilted Szekeres spacetimes
• The KBC Void: Consistency with Supernovae Type Ia and the Kinematic SZ Effect in a $\Lambda$LTB Model
• Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data
• Gravitational entropies in LTB dust models
• Symmetries and Singularities of the Szekeres System
• Coarse-grained description of cosmic structure from Szekeres models
• Invariant characterization of the growing and decaying density modes in LTB dust models
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Cosmological backreaction within the Szekeres model and emergence of spatial curvature
• Apparent horizons in the quasi-spherical Szekeres models
• Constructing Realistic Szekeres Models from Initial and Final Data
• On spherical dust fluctuations: the exact vs. the perturbative approach
• Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy
• Symmetry and Equivalence in Szekeres Models
• Testing the Copernican Principle with Hubble Parameter
• Modelling Inhomogeneity in Szekeres Spacetime
• Quantization of inhomogeneous spacetimes with cosmological constant term
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Gravitational entropy of local cosmic voids
• Frame Rotation in the Szekeres Spacetimes
• Emergence of spatial curvature
• Effects of anisotropy on gravitational infall in galaxy clusters using an exact general relativistic model
• Szekeres models: a covariant approach
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
• Weighed scalar averaging in LTB dust models, part II: a formalism of exact perturbations
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Inhomogeneous spacetimes in Weyl integrable geometry with matter source
• The environment-dependence of the growth of the most massive objects in the Universe
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Gravitational entropy of cosmic expansion
• Detecting cosmic voids via maps of geometric-optics parameters
• Cosmological perturbations on an averaged background
• An effective $\mathbf{\Lambda }$-Szekeres modelling of the local Universe with Cosmicflows-4
• An invariant characterization of the quasi-spherical Szekeres dust models
• Observer-based invariants for cosmological models
• Gravitational Entropy in Szekeres Class I Models