Relative stability in critical collapse of scalar fields with angular momentum

We study numerically the gravitational collapse of two massless scalar fields in spherical symmetry using an approach which incorporates some of the effects of angular momentum. Each field is characterized by a distinct angular momentum parameter, l, with l = 0, 1, 2, ..., and has distinct equations of motion. We focus on black critical behaviour, in which we look for solutions, and the properties thereof, that represent the onset of black hole formation in parametrized families of initial data. Although many different critical solutions have been discovered since the early 1990's, almost all work has involved a single matter source, and by coupling more than one type of matter to the gravitational field, new and interesting questions arise. In particular, we consider the issue of the relative stability of the critical solutions in our model, in which we look for signs of instability of one field in the presence of the critical solution associated with the other. Our main result is that fields corresponding to larger values of l appear to be unstable in the context of lower-l critical solutions. This implies that in a two-field universe, the field with larger l would always dominate at precise criticality.Science, Faculty ofPhysics and Astronomy, Department ofGraduat