Relativistic Gravitation and Astrophysics

自从2015年首次探测到来自合并黑洞的引力波以来，引力波科学已经成为天文学中一个新的、充满活力的分支。除了为探索开辟了新的途径，比如宇宙黑洞的起源，它还为爱因斯坦的广义相对论提供了新的检验。天文学家对超大质量黑洞（如银河系中心的黑洞）附近恒星和气体运动的观测，也为在时空扭曲极端的领域测试爱因斯坦的理论提供了可能性，并提出了恒星如何在这种极端物体附近形成和演化的问题。然而，为了验证爱因斯坦的伟大理论，有必要知道它对实际测量的实际预测。这个项目继续了一项研究计划，旨在为爱因斯坦理论的抽象之美和复杂数学与物理学家和天文学家进行测量的现实世界之间提供具体联系。这些联系是通过找到近似的、精确的、实用的形式的方程解来建立的。这项研究的结果将被引力波天文台的数据专家用来利用新探测到的信号对广义相对论进行更好的测试，并将被天文学家用来探测广义相对论如何影响复杂的系统，比如围绕超大质量黑洞运行的恒星，或者涉及从黑洞到系外行星的三体系统。爱因斯坦的理论是一个让公众着迷的话题，PI将继续就与这项研究相关的主题进行公开讲座，让更广泛的社区了解爱因斯坦的思想。具体来说，这个项目将有助于地面引力波观测站，如LIGO-Virgo-Kagra网络，通过计算二元系统发出的引力波来测试广义相对论，这是一个重要的替代理论，被称为爱因斯坦-以太引力，在所谓的后牛顿近似中达到高精度。该项目将继续扩展PI最近的工作，将爱因斯坦理论的影响纳入三体系统的动力学，例如银河系核心的双黑洞系统，其中心有一个超大质量黑洞。一个具体的目标是观察围绕银河系中心黑洞旋转的被称为SO-2的恒星是否可以用来探测或限制在超大质量物体周围轨道上假设的中等质量黑洞。另一个项目是在第二后牛顿近似下研究n体系统中的广义相对论效应，目的是评估相对论效应如何影响致密恒星系统的长期稳定性。该奖项反映了美国国家科学基金会的法定使命，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，被认为值得支持。

Since the first detection of gravitational waves from merging black holes in 2015, gravitational-wave science has emerged as a new and vibrant branch of astronomy. In addition to opening new avenues for exploration, such as the origin of cosmic black holes, it has yielded new tests of Einstein’s general theory of relativity. Observations by astronomers of the motions of stars and gas near supermassive black holes, such as the one at the center of the Milky Way, have also opened the possibility of testing Einstein’s theory in realms where the warping of spacetime is extreme, and raised questions about how stars form and evolve near such extreme objects. Yet in order to test Einstein’s great theory, it is essential to know what it actually predicts for real measurements. This project continues a program of research to provide concrete links between the abstract beauty and complex mathematics of Einstein’s theory and the real world where measurements are made by physicists and astronomers. These links are established by finding approximate, yet accurate solutions of the equations in forms that are practical and usable. The outcomes of this research will be used by data experts at the gravitational-wave observatories to perform better tests of general relativity using newly detected signals, and will be used by astronomers to probe how general relativity affects complex systems such as stars orbiting supermassive black holes, or three-body systems involving bodies ranging from black holes to exoplanets. Einstein's theory is a topic that fascinates the general public, and the PI will continue to give public lectures on topics related to this research, bringing understanding of Einstein's ideas to the broader community.Specifically, this project will contribute to the ability of ground-based gravitational-wave observatories such as the LIGO-Virgo-Kagra network to test general relativity, by computing the gravitational waves emitted by binary systems as predicted by an important alternative theory, known as Einstein-Aether gravity, to high accuracy in the so-called post-Newtonian approximation. The project will continue to extend recent work of the PI on incorporating the effects of Einstein’s theory into the dynamics of three-body systems, such as a binary-black-hole system in a galactic core with a supermassive black hole at its center. A specific goal is to see whether observations of the star known as SO-2 which revolves around the galactic center black hole can be used to detect or limit a hypothetical intermediate-mass black hole in orbit around the supermassive object. Another project is to study general relativistic effects in N-body systems at the second-post-Newtonian approximation, with the goal of assessing how relativistic effects impact the long-term stability of dense stellar systems.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.