TIME-LIKE SELF-SIMILAR SPHERICALLY SYMMETRICAL PERFECT-FLUID MODELS

Einstein's field equations for timelike self-similar spherically symme tric perfect-fluid models are investigated. The field equations are re written as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of eq uations in the coupled system is reduced as far as possible and so tha t the reduced phase space becomes compact and regular. The system is s ubsequently analysed qualitatively using the theory of dynamical syste ms. Using this approach, we obtain a clear picture of the full phase s pace 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.