A Numerical Study of the Time Dependent Schroedinger Equation Coupled with Newtonian Gravity
Abstract
The dynamical study of a massive scalar field in the Newtonian regime could produce some interesting insights into the nature of bosonic matter. Since most of the dark matter in the universe is believed to be nonbaryonic in nature, the study of bosonic matter in the form of a massive bose condensate, boson stars, could lead into insights into dark matter. In this dissertation, I discuss a numerical study of the dynamics of a massive complex scalar field in three spatial dimensions. As the general relativistic equations are too complex to solve as part of an initial study, I move to the Newtonian regime where the behavior of the scalar field is described by the time dependent Schrodinger equation coupled with Newtonian gravity. I use an alternating directions implicit (ADI) finite difference method use to solve the Schrodinger equation while using a multigrid method to solve Poisson's equation. I then discuss how to check the convergence of the difference equations with the unknown analytic solution; a technique particularly useful due to the richness of the solution space of difference equations. I show that the difference solutions in this dissertation are valid where the matter distribution is well resolved and the approximate boundary conditions have little effect on the order of convergence of the interior finite difference equations. Using boundary conditions which are valid at infinity on a finite computational domain causes errors in the solution. To stem this problem for the Schrodinger equation I developed a new technique for allowing matter to flow out of the computational domain and show the method is shown to be quite robust even in three dimensions. Finally, a numerical study of the dynamics of boson stars is given. It is found that the stars exhibit behavior similar to that of a point Newtonian mass as well as a collisionless fluid.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........25G
 Keywords:

 BOSONS;
 Physics: Astronomy and Astrophysics