Geometry and topology of the quasi-plane Szekeres model

Abstract

This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasi-hyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the $t=$ const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Interpretation of the mass function in the quasi-plane model.

14 pages, 6 figures; old sections 8, 10 and 11 removed, the remaining ones re-edited for consistency. This is a corrected version that takes into account the erratum published in Phys.Rev. D85, 069903(E) (2012)

References in corpus (8)

• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• CMB Anisotropy of the Poincare Dodecahedron
• CMB Anisotropy of Spherical Spaces
• Structure formation in the quasispherical Szekeres model
• Evolution of cosmic structures in different environments in the quasispherical Szekeres model
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Predicting the CMB power spectrum for binary polyhedral spaces

Cited by in corpus (19)

• Inhomogeneous cosmological models: exact solutions and their applications
• Average expansion rate and light propagation in a cosmological Tardis spacetime
• Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model
• A novel approach to the dynamics of Szekeres dust models
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
• Vorticity and entropy production in tilted Szekeres spacetimes
• Volume averaging in the quasispherical Szekeres model
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Symmetry and Equivalence in Szekeres Models
• Modelling Inhomogeneity in Szekeres Spacetime
• Frame Rotation in the Szekeres Spacetimes
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Geometry of the quasi-hyperbolic Szekeres models
• Does spatial flatness forbid the turnaround epoch of collapsing structures?
• Existence of blueshifts in quasi-spherical Szekeres spacetimes
• Quasilocal horizons in inhomogeneous cosmological models