Problems in Numerical Relativity

各种广义相对论系统将使用计算技术进行研究：研究将集中在引力坍缩，黑洞动力学和软件基础设施的开发，以支持在数值相对论和其他领域的一般大规模计算的关键现象。 黑洞临界现象的研究涉及到1、2、3维空间中的时间相关计算。 一维计算将用于研究理想流体和多标量坍缩中临界现象的本质，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，轴对称的广义相对论代码（包括旋转）将被构造和用于研究轴对称的临界现象。 该代码将结合耦合到标量和电磁场，并将用于搜索新的临界解，回答有关非球形扰动的球对称临界解的稳定性的重要问题，并调查角动量在临界崩溃中的作用。 还将与参与二元黑洞大挑战工作的其他研究人员合作，对全三维背景下的临界行为进行初步研究。 对黑洞动力学的研究将侧重于确定适合于模拟一般黑洞遭遇的坐标系的问题。 黑洞切除技术，其中的计算域被构造成与事件视界之外的时空区域大致重合，将进一步发展和使用这些坐标系。 将实施和严格测试用于大规模并行硬件的自适应网格算法。 这项工作最初将在相对简单的非相对论玻色子星通过牛顿引力场相互作用的模型的背景下进行。 还将继续努力建立快速原型环境，以解决一般的时间相关有限差分系统，并开发软件，对大规模计算的输出进行分析和可视化。

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.