Collaborative Research: Developing Spectral Methods for Simulating Binary Black Hole Spacetimes

这项研究将继续由加州理工-康奈尔数值相对论合作开发光谱爱因斯坦代码。谱方法对于具有光滑解的问题是理想的，比如真空爱因斯坦方程。光谱方法的指数收敛将为使用当前可用的计算机硬件进行LIGO和LISA数据分析提供所需的精度。将对该代码进行一系列关键的改进和增强：这项工作预计将允许代码模拟双黑洞的合并阶段；将实现更有效的域分解；改进将允许代码模拟具有不等质量和不等自旋的双黑洞系统；求解二阶双曲演化系统的能力将被添加到代码中；将包括一个视界探测器；将增加隐式时间步进，使代码能够更有效地跟踪双黑洞演化的绝热吸气阶段；规范使用的外边界条件将得到改善；将构建更多与天体物理学相关的初始数据；将开发新的方法来描述和定量比较不同小组使用不同数值代码产生的数值模拟结果。这项研究将对计算科学的更广泛领域产生重大影响。所开发的计算技术可用于解决许多其他领域的问题，包括流体动力学、气象学、地震学和天体物理学。在这些技术方面受过训练的年轻研究人员需求量很大。这笔资金将用于培养研究生和博士后。这项研究还将对基础物理学的理解产生广泛的影响：目前还没有在黑洞强场范围内对广义相对论进行真正的测试。对于像LIGO这样将理论与观测相对抗的实验来说，人们必须能够计算出理论所预测的结果，从而回答以下问题：LIGO可能观测到的黑洞真的是爱因斯坦理论所预测的黑洞吗？

This research will continue the development of the Spectral Einstein Code by the Caltech-Cornell numerical relativity collaboration. Spectral methods are ideal for problems with smooth solutions, like the vacuum Einstein equations. The exponential convergence of spectral methods will provide the needed accuracy for LIGO and LISA data analysis using currently available computer hardware. A series of crucial improvements and enhancements to this code will be made: This work is expected to allow the code to model the merger phase of binary black hole simulations; more efficient domain decompositions will be implemented; enhancements will be made that allow thecode to simulate binary black hole systems with unequal masses and unequal spins; the ability to solve second-order hyperbolic evolution systems will be added to the code; an event horizon finder will be included; implicit time stepping will be added to allow the code to follow the adiabaticinspiral phase of binary black hole evolutions more efficiently; the outer boundary conditions used by the code will be improved; more astrophysically relevant initial data will be constructed; new methods will be developed to characterize and quantitatively compare the results of numerical simulations produced by different groups using different numerical codes.This research will have a significant impact on the broader area of computational science. The computational techniques developed could be used to solve problems in many other areas, including fluid dynamics, meteorology, seismology, and astrophysics. Young researchers trained inthese techniques are in great demand. The funds from this grant will support the training of graduate students and postdoctoral scholars. This research will also have a broad impact on the understanding of fundamental physics: There are currently no real tests of general relativity in the strong field regime of black holes. For experiments like LIGO to confront theory with observation, one must be able to calculate what the theory predicts to answer questions such as: Are the black holes that LIGO may observe reallythe black holes predicted by Einstein's theory?