O Some Features of the Five-Dimensional Witten Bubble Spacetime

It has been suggested that the 'naive' vacuum state of five-dimensional general relativity, having the topology M^4times S^1, may be unstable against topology-changing semiclassical decay. An alternative vacuum state, herein referred to as the 'Witten bubble', has been proposed. The present work attempts to address several features associated with the interaction of this alternative vacuum with matter of various forms. By way of preparation for such an investigation, we begin by discussing the geometry of the Witten bubble spacetime, and consider how ordinary classical test particles interact with the bubble. Next, we apply the method of Bogoliubov transformations, together with certain simplifying assumptions, to obtain approximate particle number and energy production due to the formation of the Witten bubble. A second, complimentary attack on the problem of quantum effects in the Witten bubble spacetime is also attempted; namely, the determination of the stress-energy-momentum tensor in this spacetime. Technical difficulties prohibit the actual solution of this problem. Thus, we obtain only an analytic expression in terms of an infinite sum-over-modes for the adiabatically regularized stress tensor, and we describe the mode functions entering into this expression. We then attempt to determine the possible 'back-reaction' of any created or pre-existing matter on the expansion of the bubble. Again, this investigation is fraught with technical difficulties; consequently only limited conclusions are reached. A final chapter summarizes the results of this work, and proposes logical extensions and improvements thereof.