CAREER: Gravitational and Electromagnetic Waves on Black Holes

数学广义相对论领域在分析爱因斯坦方程的解方面发挥了基础性作用，例如黑洞--黑洞可以说是我们理解宇宙中最基本的物体之一。了解黑洞的稳定性一直是确认它们与现实物理对象的相关性的数学努力的核心。如果是稳定的，被引力或其他形式的辐射扰动的黑洞，经过暂时的变化，最终会回到它们的初始状态。这位研究人员的目标是通过包括电磁辐射与引力波的相互作用来促进对微扰动力学的现有知识。这种相互作用是重要的，因为天体物理黑洞被认为是被物质的吸积盘包围的，尤其是包含电磁波的物质。这项工作的成果通过同行评议的出版物和研讨会与数学界和物理界分享，并通过媒体文章、公开讲座和学校外展活动向公众传播。调查员的研究与教育活动相结合，以增加妇女在数学方面的代表性，并促进学生对数学的参与。研究生和博士后也将参与这项研究。该项目的重点是建立一种全面的方法来分析旋转和带电黑洞上引力波和电磁辐射之间的相互作用。通过发展一种包含耦合波动方程组的能量-动量张量的通用方法，研究者结合了新的技术来获得带电黑洞上的引力波和电磁波的精确衰减。该项目的目标是证明最一般的带电旋转黑洞族的非线性稳定性，并扩大研究人员在解决科尔族问题上的合作工作。此外，研究人员的目标是获得荷电黑洞的与其正则能量相关的守恒定律，同时允许控制无限大辐射的引力和电磁能量。这一裁决反映了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。

The field of Mathematical General Relativity has played a fundamental role in the analysis of solutions to the Einstein equation, such as black holes - arguably one of the most fundamental objects in our understanding of the universe. Understanding stability of black holes has been central to the mathematical endeavor of confirming their relevance as realistic physical objects. If stable, black holes perturbed with gravitational or other form of radiation, after a temporary change, would eventually return to their initial state. The investigator aims to advance the current knowledge of perturbations dynamics by including interaction of electromagnetic radiation with gravitational waves. This interaction is significant as astrophysical black holes are thought to be surrounded by an accretion disk of matter which, in particular, contains electromagnetic waves. The results of this work are shared with the mathematical and physical communities through peer-reviewed publications and seminars and disseminated to the general public through media articles, public lectures and outreach events in schools. The research of the investigator is integrated with educational activities that increase representation of women in mathematics and promote engagement in mathematics among students. Graduate students and postdocs are also to be involved in this research. The project is focused on building a comprehensive approach to analyze interactions between gravitational waves and electromagnetic radiation on rotating and charged black holes. The investigator incorporates new techniques to obtain precise decay for the gravitational and electromagnetic waves on charged black holes by developing a universal method involving a combined energy-momentum tensor for coupled system of wave equations. The goal of the project is to prove the non-linear stability of the most general charged and rotating black hole family and extend the investigator’s collaborative work on the resolution for the Kerr family. In addition, the investigator aims to obtain conservation laws for charged black holes in connection with their canonical energy while allowing control of the gravitational and electromagnetic energy radiated at infinity.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.