MATHEMATICAL PROBLEMS IN GENERAL RELATIVITY

Stanford University, Stanford CA

Investigators

Abstract

The project aims at studying various aspects of the Einstein equations, which govern the dynamics of spacetime geometry in general relativity. The PI is particularly interested in studying the solution regimes where gravity is very strong, including in the presence of spacetime singularities, as well as settings where there is a strong interaction between matter fields (such as stars and gases) and gravity. Broader impacts include work with students, and the project presents some questions that are believed to be ready for research by graduate students. THe PI seeks to answer a series of questions in this project. What does the singular boundary of generic black holes look like? What happens to the singular boundary when matter fields are present, and what happens to the matter fields themselves near the singular boundary? How do self-gravitating "null shells of matter fields propagate and interact? How does shock form in self-gravitating gas? While solving these problems, the PI will develop mathematical tools useful for hyperbolic partial differential equations beyond the application in general relativity. 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.