Problems in Numerical Relativity

将使用计算技术研究各种广义相对论系统：研究将集中在引力塌缩、黑洞动力学以及开发软件基础设施以支持数值相对论和其他领域的通用大规模计算方面的关键现象。对黑洞临界现象的研究将涉及L、2维和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塌中临界现象的性质，以及在其他物质场存在时各种球对称临界解的稳定性。构造了一种新的自适应的轴对称广义相对论代码(包括旋转)，并用于研究轴对称中的临界现象。该程序将包括与标量场和电磁场的耦合，并将用于寻找新的临界解，回答有关非球扰动的球对称临界解的稳定性的重要问题，以及研究角动量在临界坍塌中的作用。还将与参与双星黑洞大挑战努力的其他研究人员合作，对全三维背景下的关键行为进行初步研究。黑洞动力学的研究将集中在确定适合于模拟一般黑洞相遇的坐标系的问题。黑洞切除技术将进一步发展，并与这些坐标系一起使用。在这些技术中，计算区域被构造为与位于事件视界之外的时空区域大致重合。用于大规模并行硬件的自适应网格算法将被实施并进行严格的测试。这项工作最初将在非相对论玻色子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依赖时间的有限差分系统而建造快速原型环境，并开发用于分析和显示大规模计算结果的软件。

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.