Dynamics of the Wyman sector in the Nonsymmetric Gravitational Theory

grantor: University of TorontoThe canonical analysis of Nonsymmetric Gravitational Theory ( NGT) is reviewed in order to provide a framework with which to examine the dynamics of the theory. This study is simplified by considering the dynamics of the Wyman sector in spherical symmetry, which is compared to the dynamics of a self-gravitating scalar field (EKG). The similarity between the two theories allows us to use the singularity theorems of General Relativity (GR) in order to equate the existence of trapped surfaces on a spacelike hypersurface with the formation of a black hole region in the spacetime. The stability of the static spherically symmetric solutions of both NGT and EKG is discussed. It is found that the Wyman solution of NGT is unstable against spherically symmetric perturbations, which excludes this as a possible endstate of a generic evolution. Furthermore, it is demonstrated that the only possible solution in NGT which is globally regular is the Minkowski solution, while the only solution with an event horizon is the Schwarzschild solution. These solutions, which are shown to be perturbatively stable, can represent such an endstate. Meanwhile, it is demonstrated that the corresponding solutions in EKG have both a stable and an unstable branch, and due to their nakedly singular nature might have implications for the Cosmic Censorship Conjecture. Finally, the spherically symmetric Wyman field equations are numerically integrated. The initial data is chosen to consist of a spherically symmetric pulse in the Wyman sector, and the results are compared to the evolution of a scalar field. In particular, it is shown that an apparent horizon does indeed form for "strong" enough initial data, and critical behaviour is observed at the threshold of black hole formation.Ph.D