ABSTRACT

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.

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