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. Bosons are promising candidates for dark matter. They can form compact objects through a Jeans instability mechanism. We studied boson stars made up of self-gravitating scalar fields, with and without nonlinear self-couplings. These are non-topological solutions of the coupled Einstein–Klein– Gordon equations. We studied the stability of boson stars in the ground and excited states, 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 possibility of a bosonic halo surrounding galaxies. These halo models predict the observed flatness of galactic curves. We studied their formation and stability. 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 3 spatial dimension (3D) study was on the validation of the numerical code constructed to solve Einstein equations with matter sources. The use of the scalar field has unique advantages: Boson Stars do not suffer from difficulties associated with hydrodynamic sources (like shock waves or the surface problems of neutron stars). They also do not suffer from the difficulties related to 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 under radial perturbations. We then went on to study their behavior under non-spherical perturbations. Both scalar and gravitational radiation produced under these perturbations were studied. 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.