# Cyclic Szekeres Universes

## TL;DR

This paper explores cyclic and static solutions in Szekeres universes with inhomogeneous dust and ghost matter, analyzing their stability and identifying conditions for cyclic cosmologies.

## Contribution

It introduces a model combining inhomogeneous dust with ghost matter in Szekeres universes, revealing new static and cyclic solutions and analyzing their stability.

## Key findings

- Existence of static and cyclic solutions in Szekeres universes.
- Identification of stability conditions for these solutions.
- Demonstration of inhomogeneous and homogeneous spacetime families.

## Abstract

We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $p_{g}=\left( \gamma-1\right) \rho_{g},$ where $\gamma$ is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universe. The ghost field Einstein permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.