Problems in Numerical Relativity

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A variety of general relativistic systems will be studied using computational techniques: research will focus on critical phenomena in gravitational collapse, black hole dynamics, and development of software infrastructure to support general large-scale computations in numerical relativity and other fields. The studies of black-hole critical phenomena will involve time-dependent computations in l, 2 and 3 spatial dimensions. The 1-d calculations will be used to investigate the nature of critical phenomena in perfect fluid and multi-scalar collapse as well as the stability of various spherically-symmetric critical solutions in the presence of other matter fields. A new adaptive, axisymmetric general relativistic code (including rotation) will be constructed and used to study critical phenomena in axisymmetry. The code will incorporate couplings to scalar and electromagnetic fields and will be used to search for new critical solutions, to answer important questions concerning the stability of spherically-symmetric critical solutions to non-spherical perturbations, and to investigate the role of angular momentum in critical collapse. Preliminary studies of critical behaviour in a fully 3- dimensional context will also be undertaken in collaboration with other researchers involved in the Binary Black Hole Grand Challenge effort. Research on black hole dynamics will focus on the issue of determining coordinate systems appropriate for the simulation of general black hole encounters. Black hole excising techniques, in which the computational domain is constructed to roughly coincide with those regions of spacetime which lie outside of event horizons, will be further developed and used in conjunction with these coordinate systems. Adaptive mesh algorithms for use on massively parallel hardware will be implemented and rigorously tested. This work will be initially performed in the context of the relatively simple model of non-relativistic boson stars interacting through the Newtonian gravitational field. Work will also continue on the construction of rapid prototyping environments for the solution of general time-dependent finite-difference systems, and on the development of software for the analysis and visualization of the output from large scale computations.