Wave Dark Matter and Dwarf Spheroidal Galaxies

We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely on a fundamental constant $\Upsilon$ (also known as the "mass term" of the Klein-Gordon equation). Specifically, in this dissertation, we study spherically symmetric wave dark matter and compare these results with observations of dwarf spheroidal galaxies as a first attempt to compare the implications of the theory of wave dark matter with actual observations of dark matter. This includes finding a first estimate of the fundamental constant $\Upsilon$. The majority of this thesis has also been presented by the author in three separate shorter papers with arXiv reference codes [arXiv:1210.5269 [gr-qc]], [arXiv:1212.6426 [gr-qc]], [arXiv:1301.0255 [astro-ph.GA]]; note that [arXiv:1301.0255 [astro-ph.GA]], and hence part of Chapter 4, represents joint work with Hubert Bray.