Problems in Gravitation

该项目继续对非常强场引力波源进行计算研究，重点是黑洞的相互作用。 爱因斯坦的广义相对论描述了相互作用的黑洞。 大多数在计算机上求解广义相对论的十个方程的方法只考虑使用其中的六个，称为演化方程。剩下的四个，称为约束方程，仍然在数学上求解，但由于计算机模拟中不可避免的数值误差，可能会成为问题。根据先前的奖项开发的各种计算算法，将在本项目中开发的其他算法，以及方程相关属性的数学研究将应用于3D约束（即使用所有十个方程）模拟相互作用的黑洞。由于第一代引力波探测器即将成熟，预测来自天体物理引力波源的波形，比如相互作用的黑洞，是必须的。最近的发展，其中一些起源于以前的工作在得克萨斯州，走到一起，允许更强大的和物理相关的源模拟。这些发展，非常重要的是，引入了爱因斯坦方程的完全约束演化。这已经成为可能，在这一领域的一系列发展，这项工作将与高中，本科生和研究生，博士后研究人员的组合完成。它将有助于科学和天体物理学的社区欣赏，特别是将有助于LIGO和丽莎引力波探测器的成功。

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.