SPHERICALLY SYMMETRICAL SPACETIMES AND KINEMATIC SELF-SIMILARITY

The perfect-fluid Einstein field equations in the case of spherical sy mmetry reduce to an autonomous system of ordinary differential equatio ns when a spacetime is assumed to admit a kinematic self-similarity (o f either the second or zeroth kind). The qualitative properties of sol utions of this system of equations, and in particular their asymptotic behaviour, are investigated. The geodesic subcase and a subcase conta ining the static models are examined in detail. In particular, exact s olutions are obtained and the asymptotic behaviour of the solutions is fully studied in these important subcases. Exact solutions admitting a homothetic vector are found to play an important role in describing the asymptotic behaviour of the kinematic self-similar models.