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

一个多世纪以来，研究人员对爱因斯坦的广义相对论(GR)--我们对引力的最好理解--进行了越来越复杂和精确的研究。随着来自高级LIGO和室女座的引力波(GW)的直接探测，当黑洞(BH)相互融合时，现在有可能在完全非线性的、动态的、强场区域内测试GR。引力波探测也开启了观察GR更微妙的方面的可能性，比如GW通过后对时空的永久形变(“记忆”)。无论是这些新测试，还是记忆的微妙影响，都需要比以前更精确的预测和更仔细的计算。具体地说，要进行GR的精度测试，需要在GR中和GR之外的理论中进行合并BH的超级计算机模拟。提高GR测试精度的一个方面是更深入地了解GR模拟中的细微影响，例如GR中的基本坐标自由度，这使得在独立模拟之间进行比较变得更加困难。该奖项研究部分的第一部分是为了更好地理解GR的这些微妙之处。至于GR以外的模拟，PI及其合作者已经开发出一种技术，用于接近GR的理论类，但这些模拟还没有发展到GR模拟的复杂程度。本奖项研究部分的第二部分将推进Beyond-GR模拟的技术水平。同时，该奖项的教育部分将支持互动可视化的发展，以帮助教育工作者向更广泛的受众教授GR和GWS。这些互动工具将在网上提供，超越课堂教育。研究的第一部分包括旨在推动数字相对论波形达到更高精度的研究，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)高精度多模准正规化拟合，特别是对于进动系统，目标是最终建立振铃替代模型；(Ii)开发一个框架，用于比较通过Bondi-Van der Burg-Metzner-Sachs(BMS)小组的变换建模后的波形，以便在不同规范下执行的模拟之间进行比较，并更好地与后牛顿或有效一体波形杂交；(Iii)从统计学上验证BMS(非)守恒定律；以及(Iv)解释准圆形双星激励发出辐射的近似对称性的存在。研究部分的第二部分侧重于推进超越引力理论的二元BH合并模拟的最新技术。该程序包括：(I)将Beyond-GR波形的产生带入“生产”模式；(Ii)通过应用数值动力重整化群来控制长期效应(由于使用微扰理论)的增长；(Iii)为Beyond-GR波形建立代理模型；以及(Iv)通过将其应用于标量张量理论来验证该机制，该理论也可以在不借助微扰理论的情况下处理。最后，教育部分涉及制作交互式可视化以帮助教授GR和GW物理原理。这些交互式可视化将包括围绕BHS运行的粒子、GW如何变形时空、GW如何投影到LIGO天线方向图，甚至BBH中的GW如何随着内部和外部参数的变化而变化。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，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.