Abstract
There exists a long standing interest in studying topological solitons that are embedded in curved spacetime. This comes from a natural pairing, the solitons tend to be stable solutions that are usually compact around their center, while the spacetimes employed are so called maximally symmetric spacetimes. Of particular interest are Higgs monopole solutions in anti de-Sitter spacetime (AdS), which have been a frequent object of study in physics. An additional benefit of working in AdS is the existence of an additional length scale corresponding to the radius of curvature, allowing the mass scales of the Higgs and its gauge field to go to zero in these Higgs type theories and ensuring that the dynamics only depend on the radius of curvature. Following on the work of Haddad and Alvarez, who studied the time-independent solutions for topological solitons embedded in AdSn, We considered the case for solutions that are time-dependent for monopole solitons embedded in AdS4. Two such cases were considered, the case where the monopole underwent a time-dependent rigid body rotation, and the case where the monopole underwent time-dependent radial oscillations. The former case was considered in Chapter 3, the action was found to separate into a component that matched the static soliton solution found by the previous work and a component that contained the time-dependence. This second component further consisted of a moment of inertia term multiplied by a time integral consisting of the square of the angular velocity. In Chapter 4 the case of radial oscillation was considered. The time-dependent action was obtained and analyzed to second order to avoid nonlinear contributions from the higher order terms. In doing so, the linearized equations of motion were found. The radial oscillation ansatz was separated into a spatial term and a temporal term with normal modes of frequency ω. Analyzing the function in the context of a Poschl-Teller problem confirmed that the normal mode frequencies followed a integer sequence and a non-divergent general solution for the normal mode oscillations was derived.