Geometry of the quasi-hyperbolic Szekeres models

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.

19 pages, 13 figures. This version matches the published text

References in corpus (4)

• Structure formation in the quasispherical Szekeres model
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Volume averaging in the quasispherical Szekeres model
• Apparent horizons in the quasi-spherical Szekeres models

Cited by in corpus (4)

• Symmetry and Equivalence in Szekeres Models
• Modelling Inhomogeneity in Szekeres Spacetime
• Frame Rotation in the Szekeres Spacetimes
• Existence of blueshifts in quasi-spherical Szekeres spacetimes