Problems in Gravitation

万有引力问题

• 批准号: 0354842
• 负责人: Richard Matzner
• 金额: $ 42万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354842&HistoricalAwards=false
• 关键词: Problems; Gravitation

This project continues a computational study of very strong field gravitational wave sources, concentrating on the interaction of black holes. Interacting black holes are described by Einstein's theory of General Relativity. Most approaches to solving the ten equations of General Relativity on the computer consider use only six of these, called the evolution equations. The remaining four, called the constraint equations, remain solved mathematically but can become problematical due to unavoidable numerical error in a computer simulation. Various computational algorithms developed under prior awards, additional ones to be developed in this project, and mathematical studies of relevant properties of the equations will be applied to a 3D constrained (i.e. using all ten equations) simulation of interacting black holes.Because the first generation of gravitational wave detectors is coming to maturity, prediction of waveforms from astrophysical gravitational wave sources, such as interacting black holes, is imperative. Recent developments, some of them originated in prior work at Texas, are coming together to allow more robust and physically relevant source simulations. These developments, very importantly, the introduction to fully constrained evolution of the Einstein equations. This has been made possible by a series of developments in this field, This work will be done with a combination of high school, undergraduate, and graduate students, and postdoctoral researchers. It will contribute to the community appreciation of science and astrophysics in particular, and will contribute to the success the LIGO and LISA gravitational wave detectors.

该项目继续对强场引力波源进行计算研究，重点关注黑洞之间的相互作用。爱因斯坦的广义相对论描述了相互作用的黑洞。在计算机上求解广义相对论的10个方程的大多数方法只考虑使用其中的6个，称为演化方程。剩下的四个，称为约束方程，仍然可以用数学方法解决，但由于计算机模拟中不可避免的数值误差，可能会变得有问题。在先前的奖励下开发的各种计算算法，本项目将开发的其他计算算法，以及对方程相关属性的数学研究将应用于相互作用黑洞的三维约束（即使用所有十个方程）模拟。由于第一代引力波探测器即将成熟，因此预测来自天体物理引力波源（如相互作用的黑洞）的波形是必要的。最近的发展，其中一些源于德克萨斯州的先前工作，正在结合在一起，允许更健壮和物理相关的源模拟。这些发展，非常重要，是对爱因斯坦方程的完全约束演化的介绍。这项工作将由高中生、本科生、研究生和博士后研究人员共同完成。它将有助于社会对科学和天体物理学的理解，并将有助于LIGO和LISA引力波探测器的成功。