| dc.description | We will show that the perfect fluid Einstein field equations in the case of spherical, plane and hyperbolic symmetry reduce to an autonomous system of ordinary differential equations when a spacetime is assumed to admit a kinematic self-similarity (of either the second or zeroth kind). The qualitative properties of solutions of this system of equations, and in particular their asymptotic behaviour, will be investigated. Some details of the nature of kinematic self-similarity will be discussed to demonstrate the importance of various subcases of the full model. In particular, the geodesic subcase and a subcase containing the static models will be examined in detail. Exact solutions in these important subcases will be given and their asymptotic behaviour fully discussed. Exact solutions admitting a homothetic vector (i.e., a self similarity of the first kind) will be shown to play an important role in describing the asymptotic behaviour of the kinematic self-similar models. The mathematical techniques developed in the examination of perfect fluid solutions will then be applied to the case of an anisotropic fluid. The special case of kinematic self-similarity of infinite type will also be discussed. | en_US |
