A numerical study of boson star binaries

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This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. Boson stars, which are static, gravitationally bound configurations of a massive complex scalar field, can be made gravitationally compact. Astrophysically, the study of gravitationally compact binaries—in which each constituent is either a neutron star or a black hole—and especially the merger of the constituents that generically results from gravitational wave emission, continues to be of great interest. Such mergers are among the most energetic phenomena thought to occur in our universe. They typically emit copious amounts of gravitational radiation, and are thus excellent candidates for early detection by current and future gravitational wave experiments. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal flatness of the 3-metric), and on the time-slicing of the spacetime (maximal slicing), and has been previously used in the simulation of neutron stars mergers. The resulting modeling problem requires the solution of a coupled nonlinear system of 4 hyperbolic, and 5 elliptic partial differential equations (PDEs) in three space dimensions and time. We approximately solve this system as an initial-boundary value problem, using finite difference techniques and well known, computationally efficient numerical algorithms such as the multigrid method in the case of the elliptic equations. Careful attention is paid to the issue of code validation, and a key part of the thesis is the demonstration that, as the basic scale of finite difference discretization is reduced, our numerical code generates results that converge to a solution of the continuum system of PDEs as desired. The thesis concludes with a discussion of results from some initial explorations of the orbital dynamics of boson star binaries. In particular, we describe calculations in which motion of such a binary is followed for more than two orbital periods, which is a significant advance over previous studies. We also present results from computations in which the boson stars merge, and where there is evidence for black hole formation.