Physical and geometrical interpretation of the ϵ0 Szekeres models

Charles Hellaby and Andrzej Krasiński
Phys. Rev. D 77, 023529 – Published 25 January 2008

Abstract

We study the properties and behavior of the quasipseudospherical and quasiplanar Szekeres models, obtain the regularity conditions, and analyze their consequences. The quantities associated with radius and mass in the quasispherical case must be understood in a different way for these cases. The models with pseudospherical foliation can have spatial maxima and minima, but no origins. The mass and radius functions may be one increasing and one decreasing without causing shell crossings. This case most naturally describes a snakelike, variable density void in a more gently varying inhomogeneous background, although regions that develop an overdensity are also possible. The Szekeres models with plane foliation can have neither spatial extrema nor origins, cannot be spatially flat, and they cannot have more inhomogeneity than the corresponding Ellis model, but a planar surface can be the boundary between regions of spherical and pseudospherical foliation.

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  • Received 11 October 2007

DOI:https://doi.org/10.1103/PhysRevD.77.023529

©2008 American Physical Society

Authors & Affiliations

Charles Hellaby*

  • Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa*

Andrzej Krasiński

  • N. Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00 716 Warszawa, Poland†

  • *cwh@maths.uct.ac.za
  • akr@camk.edu.pl

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Vol. 77, Iss. 2 — 15 January 2008

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