Timelike self-similar spherically symmetric perfect-fluid models

Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems.

Using this approach, we obtain a clear picture of the full phase space and the full space of solutions. Solutions of physical interest, e.g. the solution associated with criticality in black hole formation, are easily singled out. We also discuss the various `band structures' that are associated with certain one-parameter sets of solutions.