CAREER: Gravitational and Electromagnetic Waves on Black Holes

职业：黑洞上的引力波和电磁波

• 批准号: 2336118
• 负责人: Elena Giorgi
• 金额: $ 45.43万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-07-01 至 2029-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2336118&HistoricalAwards=false
• 关键词: CAREER; Gravitational; Electromagnetic; Waves; Black

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.

数学一般相对性领域在分析爱因斯坦方程的解决方案的分析中发挥了基本作用，例如黑洞 - 可以说是我们对宇宙的理解中最基本的对象之一。理解黑洞的稳定性是确认其与现实物理对象相关性的数学努力的核心。如果稳定，则在暂时变化后用重力或其他形式的辐射干扰的黑洞最终将恢复到其初始状态。研究者旨在通过包括电子辐射与重力波的相互作用来提高目前对扰动动力学的知识。这种相互作用是显着的，因为天体物理黑洞被认为被物质的积聚磁盘包围，特别是包含电子波。这项工作的结果通过同行评审的出版物和准则与数学和物理社区共享，并通过学校中的媒体文章，公共讲座和外展活动传播给公众。研究人员的研究与教育活动融合在一起，这些活动增加了女性在数学方面的代表性，并促进学生之间的数学参与。研究生和博士后还将参与这项研究。该项目的重点是建立一种综合方法，以分析重力波和电磁辐射之间在旋转和带电的黑洞上的相互作用。研究者结合了新技术，以通过开发通用方法来获得带电黑洞的引力和电磁波的精确衰减，涉及一种用于波浪等式耦合系统的能量弹药量。该项目的目的是证明最通用和旋转的黑洞家族的非线性稳定性，并扩展了调查员在Kerr家族的决议方面的合作工作。此外，研究人员的目标是获得与其规范能量有关的带电黑洞的保护法律，同时允许在Infinity散发出的引力和电磁能量。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛的影响审查标准来通过评估来通过评估来支持的。