Conformally invariant relativistic solutions.

Abstract

The study of exact solutions to the Einstein and Einstein-Maxwell field equations, by imposing a symmetry requirement on the manifold, has been the subject of much recent research. In this thesis we consider specifically conformal symmetries in static and nonstatic spherically symmetric spacetimes. We find conformally invariant solutions, for spherically symmetric vectors, to the Einstein-Maxwell field equations for static spacetimes. These solutions generalise results found previously and have the advantage of being regular in the interior of the sphere. The general solution to the conformal Killing vector equation for static spherically symmetric spacetimes is found. This solution is subject to integrability conditions that place restrictions on the metric functions. From the general solution we regain the special cases of Killing vectors, homothetic vectors and spherically symmetric vectors with a static conformal factor. Inheriting conformal vectors in static spacetimes are also identified. We find a new class of accelerating, expanding and shearing cosmological solutions in nonstatic spherically symmetric spacetimes. These solutions satisfy an equation of state which is a generalisation of the stiff equation of state. We also show that this solution admits a conformal Killing vector which is explicitly obtained.