Beyond Stability of Black Holes in General Relativity

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This project strives to answer fundamental questions about strong field dynamics in general relativity, including black hole processes and the formation and structure of spacetime singularities. These questions can be expressed in mathematics and the project will contribute to the venerable tradition of rigorous mathematics making fundamental statements about our physical world, a tradition which in the long run has proven central to advances in science and technology. The subject of black holes and spacetime singularities has inspired the popular imagination well beyond the confines of the scientific community, as was apparent in the public reception of the detection of gravitational waves from binary black hole systems and, most recently, of the first stunning images of the immediate vicinity of a supermassive black hole. The PI and co-PI will also contribute to broader impacts via training of PhD students on problems related to the research in this project.This project strives to advance beyond the study of stability problems in general relativity and answer fundamental questions about strong field dynamics of the theory, including non-linear aspects of gravitational scattering, the fine structure of gravitational radiation and the nature of spacetime singularities. The first major objective of this project, based on a long sequence of previous joint work of the proposers, is to finish up the mathematical proof of the non-linear stability of the Kerr black hole metric. The second major objective of this project concerns understanding the structure of spacetime singularities inside black holes, aiming to understand their general form, in particular, whether they eventually become strong and spacelike. A third and final major objective concerns the question of whether singularities exist in the vacuum which are not hidden in black holes. The project aims to answer this question in the affirmative, investigating also the stability of these singularities.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.