Dynamical systems approach to relativistic spherically symmetric static perfect fluid models

We investigate relativistic spherically symmetric static perfect fluid models with barotropic equations of state that are asymptotically polytropic and linear at low and high pressures, respectively. We generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. This is accomplished by introducing dimensionless variables that are asymptotically homology invariant in the low pressure regime, which yields a reformulation of the field equations into a regular dynamical system on a three-dimensional compact state space. A global picture of the solution space is thus obtained which makes it possible to derive qualitative features and to prove theorems about massradius properties. Moreover, the framework is also suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.