Geometry of the quasi-hyperbolic Szekeres models

TL;DR

This paper explores the geometric properties of quasi-hyperbolic Szekeres models, comparing them with quasi-spherical models, analyzing their mass functions, and illustrating their shapes through graphical examples.

Contribution

It provides a detailed geometric analysis of quasi-hyperbolic Szekeres models and relates their properties to quasi-spherical models, including the role of the mass function.

Findings

Shapes of coordinate surfaces illustrated in graphs

Mass function $M(z)$ determines average density

Comparison between hyperbolically symmetric and general cases

Abstract

Geometric properties of the quasi-hyperbolic Szekeres models are discussed and related to the quasi-spherical Szekeres models. Typical examples of shapes of various classes of 2-dimensional coordinate surfaces are shown in graphs; for the hyperbolically symmetric subcase and for the general quasi-hyperbolic case. An analysis of the mass function $M(z)$ is carried out in parallel to an analogous analysis for the quasi-spherical models. This leads to the conclusion that $M(z)$ determines the density of rest mass averaged over the whole space of constant time.