# Dynamical system analysis of Einstein-Skyrme model in a Kantowski-Sachs spacetime

## TL;DR

This paper analyzes the dynamical behavior of the Einstein-Skyrme model within a Kantowski-Sachs spacetime by transforming the field equations into an autonomous system, identifying critical points, and studying their stability and bifurcations.

## Contribution

It introduces a novel dynamical systems approach to the Einstein-Skyrme model in Kantowski-Sachs spacetime, including stability analysis and bifurcation scenarios.

## Key findings

- Identification of critical points and their stability properties.
- Flow analysis on the Poincaré sphere reveals behavior at infinity.
- Use of Center Manifold Theory for non-hyperbolic points.

## Abstract

We consider a Skyrme fluid with a constant radial profile in locally rotational Kantowski-Sachs spacetime. We choose a suitable change of variable so that the Field equations modified to an autonomous system. Then we finds the critical points and inspect the stability of them. Finally, the flow on the Poincar{\'{e}} sphere is shown and consequently the behavior at infinity is determined. To analyze the non-hyperbolic critical points Center Manifold Theory has been used. Possible bifurcation scenarios also have been explained.