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

这项研究将继续由Caltech-Cornell数值相对论合作开发频谱爱因斯坦代码。谱方法对于具有光滑解的问题是理想的，例如真空爱因斯坦方程。 谱方法的指数收敛将为使用当前可用的计算机硬件的LIGO和丽莎数据分析提供所需的精度。 将对该代码进行一系列重要的改进和增强：预计这项工作将使代码能够模拟二元黑洞模拟的合并阶段;将实施更有效的区域分解;将进行增强，使代码能够模拟质量不等和自旋不等的二元黑洞系统;将在代码中增加求解二阶双曲演化系统的能力;将包括一个事件视界探测器;将增加隐式时间步进，使代码能够更有效地跟踪二元黑洞演化的绝热螺旋阶段;将改进代码使用的外边界条件;将编制更多与天体物理学有关的初始数据;将开发新的方法来表征和定量比较不同小组使用不同的方法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。计算技术的发展可以用来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。对受过这些技术训练的年轻研究人员的需求量很大。这笔赠款的资金将用于支持研究生和博士后学者的培训。 这项研究也将对基础物理学的理解产生广泛的影响：目前还没有真实的在黑洞强场区对广义相对论进行测试。对于像LIGO这样的实验来说，要想让理论与观测相对抗，人们必须能够计算出理论预测的内容，以回答这样的问题：LIGO可能观测到的黑洞真的是爱因斯坦理论预测的黑洞吗？

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?