Nonlinear Fields, Slowly Changing Geometries, and Conformal Scalings in General Relativity.

Three problems in general relativity are presented. These are (i) a numerical evolution of a nonlinear scalar field on a Schwarzschild background, (ii) the development of a perturbation technique for slowly changing axially symmetric geometries, and (iii) the study of the relationship of the conformal properties of general relativity due to the conformal scaling of the spatial three-metric and the conformal scaling of the full spacetime metric. The relevance of these three topics to contemporary problems and ideas in general relativity is discussed.