4 A Numerical Study of Boson Stars

In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Date ABSTRACT ii ABSTRACT In this thesis 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. Boson stars are localized solutions of the equations governing a massive complex scalar field coupled to the gravitational field. They can be simulated using more straightforward numerical techniques than are required for fluid stars. In particular, the evolution of smooth initial data for a scalar field tends to stay smooth, in sharp contrast to hydrodynamical evolution, which tends to develop discontinuities, even from smooth initial conditions. At the same time, relativistic boson stars share many of the same features with respect to the strong-field gravitational interaction as their fermionic counterparts. A detailed study of their dynamics can thus potentially lead to a better understanding of the dynamics of compact fermionic stars (such as neutron stars), while the relative ease with which they can be treated numerically makes them ideal for use in theoretical studies of strong gravity. In this last vein, 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, in which the black hole mass jumps discontinuously at threshold, were previously observed in the dynamics of spherically symmetric boson stars by Hawley and Choptuik [1, 2]. 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 …