A Numerical Study of Boson Stars
  We present a numerical study of general relativistic boson stars in both spherical symmetry and axisymmetry. We consider both time-independent problems, involving the solution of equilibrium equations for rotating boson stars, and time-dependent problems, focusing on black hole critical behaviour associated with boson stars.   The study of the critical phenomena that arise at the threshold of black hole formation has been a subject of intense interest among relativists and applied mathematicians over the past decade. Type I critical phenomena were previously observed in the dynamics of spherically symmetric boson stars by Hawley and Choptuik. We extend this work and show that, contrary to previous claims, the subcritical end-state is well described by a stable boson star executing a large amplitude oscillation with a frequency in good agreement with that predicted for the fundamental normal mode of the end-state star from linear perturbation theory.   We then extend our studies of critical phenomena to the axisymmetric case, studying two distinct classes of parametrized families of initial data whose evolution generates families of spacetimes that ``interpolate'' between those than contain a black hole and those that do not. In both cases we find strong evidence for a Type I transition at threshold, and are able to demonstrate scaling of the lifetime for near-critical configurations of the type expected for such a transition. This is the first time that Type I critical solutions have been simulated in axisymmetry. 
Chi-Wai Lai