Black holes and radiative fields in general relativity

In this thesis we numerically construct solutions to Einstein's equation that represent two different types of radiative fields. The first is a non-vacuum Klein-Gordon scalar field in a spherically symmetric spacetime and the second is a vacuum Brill gravitational wave in an axisymmetric spacetime.; The physical properties of the spacetimes that can arise from such constructions are analysed in a number of different coordinate systems. The initial data and evolution of both small and large amplitude waves are examined. The conditions under which collapse to black holes occurs is studied for both types of waves, along with the accuracy and convergence of the schemes used.; The evolution of Klein-Gordon scalar waves is found to agree with other numerically generated results and some further cases are examined. New results concerning the measurement of trapped surfaces and apparent horizons are presented. The evolution of the Brill waves is found to act in a similar manner for both small and large amplitude initial data sets and the behavior of trapped surfaces formed by gravitational collapse is studied.