Analyzing Boson Stars Using the Variational Method

We use the variational method to analyze properties of gravitationally bound Bose Einstein condensates called boson stars which are potential candidates for dark matter. Using a set of qualitative and quantitative measures, we compare various ansatze found in the literature in order to determine the best fit solutions for a given regime or analysis. We then use the best fit ansatze found to further study these systems. Such studies include boson star decay rates and lifetimes, dense configurations, and both special and general relativistic corrections to the relevant equations of motion. We also analyze how multiple flavor dark matter theories can account for the galactic core density-radius scaling relation which can be found in the literature from observations of galactic profiles. Through these analyses we hope to gain insights into the viability of boson stars as possible candidates for dark matter and the possible parameter spaces in which these systems can be detected.