RUI: Investigating Gravitational Waves and Extreme Mass-Ratio Compact Binaries

该奖项支持对引力波（GWs）的理论研究，这些引力波是由恒星质量致密物体（如中子星或黑洞）吸入超大质量黑洞时发出的。这些极端质量比激励（EMRIs）是重要的gw天文源，将被即将到来的激光干涉仪空间天线（LISA）探测器观测到，该探测器由美国宇航局和欧洲航天局合作开发。该项目涉及追求一种新的数学建模方法，能够以避免在先前工作中遇到的技术障碍的方式实现改进的真实感。通过该奖项实施的精确EMRI模型将使LISA观测能够以前所未有的方式揭示引力相互作用的内部工作原理。这项工作涉及对本科生研究人员的定量技术技能的直接培训，这些技能高度可转移到其他领域的STEM相关职业。该奖项支持一项协同物理教育研究项目，该项目将同时改善高等本科物理教学，并为研究新的数学建模技术提供一个试验场。该奖项的研究目标是利用PI研究小组最近发现的一种新的自我力（SF）计算方法，确定相对论性两体相互作用如何影响EMRIs的动力学。通过应用黑洞摄动理论（BHPT）将施加在次级体上的引力场和相关SF扩展到适当的小质量比幂次，精确地剖析了控制EMRIs的两体相互作用。本项目所追求的新方法涉及通过求解椭圆偏微分方程（PDEs）来计算克尔度量摄动，从而避免了先前在洛伦兹规范自力计算中遇到的数值不稳定性。这些不稳定性是通过进入频域来避免的，在频域中，场方程只涉及r和θ的导数，并且是数值求解的。本项目将研究并实现一阶洛伦兹规范克尔引力SF的椭圆PDE SF计算方法，为开始探索所需的二阶克尔SF开辟了一条途径。该项目的完成将增强对引力物理和EMRI动力学的基本理解，有助于GW数据分析，并以前所未有的精度揭示强场重力的基础。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。

This award supports theoretical investigations of the gravitational waves (GWs) emitted when a stellar mass compact object, such as a neutron star or black hole, inspirals into a supermassive black hole. These extreme mass-ratio inspirals (EMRIs) are important astronomical sources of GWs that will be observed by the upcoming Laser Interferometer Space Antenna (LISA) detector, which is under cooperative development by NASA and the European Space Agency. This project involves pursuit of a new approach to mathematical modeling that is able to achieve improved realism in a way that avoids technical hindrances encountered in prior work. Accurate EMRI models implemented through this award will enable LISA observations to reveal the inner workings of gravitational interactions like never before. This work involves direct training of quantitative technical skills for undergraduate student researchers, which are highly transferable to STEM related careers in other sectors. This award supports a synergistic physics education research project that will simultaneously improve upper-level undergraduate physics instruction and provide a testing ground to research new mathematical modeling techniques. The research objective of this award is to determine how relativistic two-body interactions influence the dynamics of EMRIs utilizing a new approach to self-force (SF) calculations recently discovered by the PI’s research group. Two-body interactions governing EMRIs are accurately dissected by applying black hole perturbation theory (BHPT) to expand the gravitational field and associated SF exerted on the secondary body up to an appropriate order in powers of the small mass-ratio. The new approach pursued by this project involves computation of Kerr metric perturbations by solving elliptic partial differential equations (PDEs), which avoids previously encountered numerical instabilities in Lorenz gauge self-force calculations. Those instabilities are avoided by entering the frequency domain, where the field equations involve only r and theta derivatives and are solved numerically. This project will research and implement the novel elliptic PDE SF method to calculate the 1st order Lorenz gauge Kerr gravitational SF, which opens a pathway to begin exploring the needed 2nd-order Kerr SF. Completion of this project will enhance fundamental understanding of gravitational physics and EMRI dynamics in ways that will assist GW data analysis and reveal the foundations of strong-field gravity with unprecedented precision.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.