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

合作研究：开发模拟二元黑洞时空的光谱方法

• 批准号: 0652995
• 负责人: Lee Lindblom
• 金额: $ 25万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0652995&HistoricalAwards=false
• 关键词: Collaborative; Research; Developing; Spectral; Methods

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?

这项研究将通过加州理工大学和康奈尔大学的数值相对论合作继续开发光谱爱因斯坦代码。谱方法是具有光滑解的问题的理想方法，例如真空爱因斯坦方程。谱方法的指数收敛将为使用现有计算机硬件的LIGO和LISA数据分析提供所需的精度。代码将有一系列重要的改进和增强：这项工作将允许代码模拟双星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，允许代码模拟具有不等质量和不等自旋的双星黑洞系统；将在代码中增加求解二阶双曲演化系统的能力；将包括事件视界探测器；将添加隐式时间步进，以使代码能够更有效地跟踪双星黑洞演化的绝热激发阶段；代码使用的外边界条件将得到改善；将构建更多与天体物理相关的初始数据；新的方法将被开发来表征和定量比较不同群体使用不同数值代码产生的数值模拟结果。这项研究将对更广泛的计算科学领域产生重大影响。开发的计算技术可以用来解决许多其他领域的问题，包括流体力学、气象学、地震学和天体物理学。受过这些技术培训的年轻研究人员需求量很大。这笔资金将用于支持研究生和博士后学者的培训。这项研究还将对基础物理的理解产生广泛的影响：目前还没有在黑洞的强场机制中真正测试广义相对论。对于像LIGO这样的实验，要想让理论与观测对抗，人们必须能够计算出理论预测的内容来回答这样的问题：LIGO可能观察到的黑洞真的是爱因斯坦理论预测的黑洞吗？