The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of s elf-similar spherically symmetric perfect-fluid models and gain a deeper un derstanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the u se of the physically interesting quantities arising in the comoving approac h. We focus on three types of models. First, we consider models that are na tural inhomogeneous generalizations of the Friedmann universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the e nergy density at later times. Secondly, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities . if naked singularities do form, they have profound implications for the p redictability of general relativity as a theory. Thirdly, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing tha t some of them are associated with the self-similar solutions associated wi th the critical behaviour observed in recent gravitational collapse calcula tions.