Relativistic hydrodynamics and other topics in numerical relativity

In this thesis I consider three different projects in numerical relativity. The first one is a study of the spherically-symmetric collapse of a scalar field with a potential that mimics the inclusion of angular momentum. This work has been carried out in collaboration with M.W. Choptuik, W. Unruh and J. Ventrella. In this study we found a new family of type II critical solutions which are discretely self similar. The second project involves work I did in another collaboration with M.W. Choptuik, L. Lehner, R. Petryk, F. Pretorius and H. Villegas. Here we study the dynamical evolution of 5-dimensional generalizations of black holes, called black strings, which are known to be unstable to sufficiently long-wavelength perturbations along the string direction. Not only have we been able to dynamically trigger the instability, explicitly verifying the results from perturbation theory, we have been able to evolve for sufficiently long times to observe that the system goes through a phase (not necessarily the final end-state) that resembles a series of black holes connected by a thin black string. The third and most extensive part of this thesis is a study of ideal fluids fully coupled to gravity, both in spherical symmetry and in axisymmetry. In this project we have cast both the dynamic and equilibrium equations for general relativistic hydrodynamics in the 2+1+1 formalism and in a way that is tailor-made for the use of high resolution shock capturing methods. In addition, our implementation, for the case of no rotation, is able to evolve discontinuous data and has proven to be convergent. Unfortunately our implementation currently has too much numerical dissipation, and suggests that the use of adaptive methods may be very helpful in achieving long term evolution of star-like configurations.Science, Faculty ofPhysics and Astronomy, Department ofGraduat