The interplay of group and dynamical systems analysis: The case of spherically symmetric charged fluids in general relativity

• Full symmetry classification of the master equation governing spherically symmetric charged fluid flow in general relativity.
• Full dynamical systems analysis of master equation in the case of one and two symmetries.
• Utilization of symmetry results to simplify the eigenvalue problem arising from dynamical systems analysis.

We investigate the relationship between the Dynamical Systems analysis and the Lie Symmetry analysis of ordinary differential equations. We undertake this investigation by looking at a relativistic model of self-gravitating charged fluids. Specifically we look at the impact of specific parameters obtained from Lie Symmetries analysis on the qualitative behaviour of the model. Steady states, stability and possible bifurcations are explored. We show that, in some cases, the Lie analysis can help to simply the dynamical systems analysis.