| dc.description.abstracteng | Dark matter is a hypothetical form of matter, which is thought to make up nearly $27\%$ of the contents in our Universe. An increasingly popular idea is that the dark matter could be composed of light (pseudo-)scalar particles with large occupation number so that they can be described by a classical scalar field $\phi$, with the mass $\approx 10^{-22}$eV. As the finite energy ground state solutions for such a field, boson stars are a good subject in the study of dark matter. In this dissertation, the primary focus is on boson stars and their surrounding miniclusters. Firstly, using my new algorithms employing the Pseudo-Spectral method, I simulate the collision of two boson stars, and find the interference pattern when two boson stars overlap. The relationship between boson stars and the surrounding miniclusters are also introduced. Secondly, I study the formation and growth of boson stars in their surrounding miniclusters by gravitational condensation using the numerical method developed. Fully dynamical attractive and repulsive self-interactions are considered for the first time. In the case of pure gravity, I numerically prove that the growth of boson stars inside halos slows down and saturates as has been previously conjectured, and detail its conditions. Self-interactions are included using the Gross-Pitaevskii-Poisson equations. We find that in the case of strong attractive self-interactions the boson stars can become unstable and collapse, in agreement with previous stationary computations. At even stronger coupling, the condensate fragments. Repulsive self-interactions, as expected, promote boson star formation, and lead to solutions with larger radii. Lastly, I simulate the formation of vortices during the merger of boson stars with gravity and find that weak attractive self-interaction can be ignored in this process. | de |