CAREER: Towards Precision Tests of General Relativity with Black Holes and Gravitational Waves

世纪以来，研究人员一直在研究爱因斯坦的广义相对论（GR）--我们对引力的最好理解--越来越复杂和精确。 通过对Advanced LIGO和Virgo的引力波（GW）的直接探测，现在可以在黑洞（BH）相互合并时在完全非线性，动力学，强场状态下测试GR。 引力波探测也开启了观察GR更微妙方面的可能性，比如GW通过后时空的永久变形（“记忆”）。 这些新的测试和记忆的微妙影响都需要比以前更高精度的预测和更仔细的计算。 具体而言，进行精度测试的GR需要执行合并BH的超级计算机模拟，无论是在GR和GR以外的理论。提高精度的GR测试的一个方面是获得更深入的了解GR模拟中的微妙影响，如GR中的基本坐标自由度，这使得独立的模拟之间的比较更加困难。 这个奖项的研究部分的第一部分是为了更好地理解这些GR的微妙之处。 至于超越GR的模拟，PI和合作者已经开发了一种技术，用于“接近”GR的理论类别，但这些模拟尚未达到GR模拟的复杂程度。 该奖项的研究部分的第二部分将推进超越GR模拟的艺术水平。 同时，该奖项的教育部分将支持交互式可视化的开发，以帮助教育工作者向更广泛的受众教授GR和GW。 这些互动工具将在网上提供，以达到课堂教育以外的研究部分的第一部分包括研究，旨在推动数值相对论波形更高的精度，而不是通过提高分辨率或模拟方法，而是通过捕捉一些微妙的影响。 这些研究包括：（i）高精度多模式准正规振铃拟合，特别是对于旋进系统，其目标是最终建立振铃代理模型;（ii）开发用于在通过Bondi-Van der Burg-Metzner-Sachs（BMS）组的变换进行建模之后比较波形的框架，用于在不同仪表中执行的模拟之间的苹果对苹果的比较，和更好的杂交与后牛顿或有效的一体波形;（iii）统计验证BMS（非）守恒定律;（iv）解释存在的近似对称性的传出辐射从准圆形二元inspirals。 研究部分的第二部分侧重于推进最先进的模拟超越GR引力理论的二元BH合并。 该计划包括：（i）将超GR波形的生成带入“生产”模式;（ii）通过应用数值动力学重整化群来控制长期效应的增长（由于使用微扰理论）;（iii）建立超GR波形的代理模型;（iv）通过将其应用于标量张量理论来验证这种机制，标量张量理论也可以在不求助于微扰理论的情况下进行处理。 最后，教育部分涉及制作交互式可视化，以帮助教授GR和GW物理学的原理。 这些交互式可视化将包括围绕BH运行的粒子，GWs如何使时空变形，GWs如何投射到LIGO天线方向图上，甚至来自BBH的GWs如何随着内在和外在参数的变化而变化。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估而被认为值得支持。

For over a century, researchers have studied Einstein's theory of general relativity (GR) -- our best understanding of gravity -- with increasing sophistication and precision. With direct detections of gravitational waves (GWs) from Advanced LIGO and Virgo, it is now possible to test GR in the fully nonlinear, dynamical, strong-field regime when black holes (BHs) merge with each other. Gravitational-wave detection also opens the possibility to observe more subtle aspects of GR, like the permanent deformation to spacetime ("memory") after a GW passes. Both these new tests and the subtle effects of memory require higher precision predictions and more careful calculations than before. Specifically, to carry out precision tests of GR requires performing supercomputer simulations of merging BHs, both in GR and in theories beyond GR. One aspect of improving the precision of tests of GR is gaining a deeper understanding of subtle effects in GR simulations, such as the fundamental coordinate freedom in GR, that makes it more difficult to compare between independent simulations. Part I of the research component of this award is to better understand these GR subtleties. As for simulations beyond GR, the PI and collaborators have developed a technique for classes of theories that are "close" to GR, but these simulations have not yet been advanced to the level of sophistication of GR simulations. Part II of the research component of this award will advance the state of the art of beyond-GR simulations. Simultaneously and independently, the educational component of this award will support development of interactive visualization to help educators teach GR and GWs to a broader audience. These interactive tools will be made available online to reach beyond classroom education.Part I of the research component consists of studies intending to push numerical relativity waveforms to higher precision, not by improving resolution or simulation methods, but rather by capturing a number of subtle effects. These studies include: (i) high-precision multi-mode quasinormal ringdown fits, especially for precessing systems, with the goal of ultimately building a ringdown surrogate model; (ii) developing a framework for comparing waveforms after modeling out by transformations of the Bondi–Van der Burg–Metzner–Sachs (BMS) group, for apples-to-apples comparisons between simulations performed in different gauges, and for better hybridization with post-Newtonian or effective-one-body waveforms; (iii) statistically validating BMS (non-)conservation laws; and (iv) explaining the existence of an approximate symmetry of outgoing radiation from quasi-circular binary inspirals. Part II of the research component focuses on advancing the state-of-the-art in simulating binary BH mergers beyond-GR theories of gravity. This program includes: (i) bringing generation of beyond-GR waveforms into "production" mode; (ii) controlling the growth of secular effects (due to using perturbation theory) by applying the numerical dynamical renormalization group; (iii) building a surrogate model for beyond-GR waveforms; and (iv) validating this machinery by applying it to scalar-tensor theory, which can also be treated without recourse to perturbation theory. Finally, the educational component involves producing interactive visualizations to help teach the principles of GR and GW physics. These interactive visualizations will include particles orbiting around BHs, how GWs deform spacetime, how GWs get projected onto LIGO antenna patterns, and even how GWs from a BBH change as the intrinsic and extrinsic parameters are varied.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.