2007/10/11 by Charles Hellaby, Andrzej Krasiński, Andrzej Krasinski · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #gr-qc
paper · pdf · doi:10.1103/physrevd.77.023529
published as Phys.Rev.D77:023529,2008 · REVTex, 21 pages, 10 figures
arxiv created 2007/10/11 · openalex publication_date 2008/01/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.