Problems in Numerical Relativity

将使用计算技术研究各种广义相对论系统：研究将集中在引力坍缩，黑洞动力学中的关键现象，以及软件基础设施的开发，以支持数值相对论和其他领域的一般大规模计算。黑洞临界现象的研究将涉及1、2和3个空间维度的随时间计算。一维计算将用于研究完美流体和多标量坍缩的临界现象的性质，以及在其他物质场存在下各种球对称临界解的稳定性。一个新的自适应的轴对称广义相对论代码（包括旋转）将被构造并用于研究轴对称中的临界现象。该代码将包含标量和电磁场的耦合，并将用于搜索新的临界解，回答有关非球面扰动的球对称临界解的稳定性的重要问题，并研究角动量在临界坍缩中的作用。在完全三维环境下的临界行为的初步研究也将与参与双黑洞大挑战努力的其他研究人员合作进行。黑洞动力学的研究将集中在确定适合模拟一般黑洞相遇的坐标系的问题上。黑洞切除技术将进一步发展，并与这些坐标系统结合使用。在这种技术中，计算域被构造成与事件视界外的时空区域大致一致。在大规模并行硬件上使用的自适应网格算法将被实现并严格测试。这项工作最初将在非相对论玻色子恒星通过牛顿引力场相互作用的相对简单模型的背景下进行。还将继续为解决一般时变有限差分系统建立快速原型环境，并开发用于分析和可视化大规模计算输出的软件。

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.