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A Numerical Study of Boson Stars: Einstein Equations with a Matter Source

The study of the properties and dynamics of self-gravitating bosonic objects in Einstein gravity was conducted. We studied self-coupled boson stars and determined the quasinormal mode (QNM) frequencies of stable boson stars in spherical symmetry. The study was carried out in the standard Einstein theory of General Relativity and in Brans-Dicke theory. We also studied the formation of these objects in Brans-Dicke theory showing that they can form from the self-gravitation of bosonic matter. We also studied the studied the possibility of a bosonic halo surrounding galaxies. After an extensive study in spherical symmetry we carried out numerical studies of boson star dynamics in full 3+1 dimension. One focus of the 3D study was on the validation of the numerical code constructed to solve Einstein equations with matter sources. Boson Stars do not suffer from the surface problems of neutron stars or the singularities of black holes. The code was first tested with spherical perturbations and compared with the spherical results. We determined the coordinate conditions needed to provide stable evolutions. We then went on to study their behavior under non-spherical perturbations. We reproduced the QNM frequencies of the stars, as determined by perturbation studies carried out by other groups. The energy generated by the perturbation was studied with different radiation indicators. We also observed the collapse to black holes of unstable boson-star configurations. We simulated the collision of two boson stars. This is of interest as the two body problem is as yet unresolved in general relativity.