Physical geometry of the quasispherical Szekeres models

Abstract

The quasispherical Szekeres metric is an exact solution to Einstein's equations describing an inhomogeneous and anisotropic cosmology. Though its governing equations are well-known, there are subtle, often-overlooked details in how the model's functions relate to its physical layout, including the shapes and relative positions of structures. We present an illustrated overview of the quasispherical Szekeres models and show exactly how the model functions relate to the physical shape and distribution of matter. In particular, we describe a shell rotation effect that has not previously been fully understood. We show how this effect relates to other known properties, and lay out some mathematical tools useful for constructing models and picturing them accurately.