Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models

Understand

The Szekeres inhomogeneous models can be used to model the true lumpy universe that we observe.

• This family of exact solutions to Einstein's equations was originally derived with a general metric that has no symmetries.
• In this work, we develop and use a framework to integrate the angular diameter and luminosity distances in the general Szekeres models.
• We use the affine null geodesic equations in order to derive a set of first-order ordinary differential equations that can be integrated numerically to calculate the partial derivatives of the null vector components.