Research in Gravitational and Mathematical Astrophysics

This award supports studies of mathematical and computational analysis methods to advance our scientific understanding of gravitational interaction. This study will focus on a series of problems where strong gravitational fields play an interesting role in a variety of astrophysical situations. These include studies of the properties of neutron stars, black holes, gravitational waves, and the large-scale structure of the universe itself. The new insights discovered by this project could have impacts in a wide range of scientific areas that extend well beyond gravitational astrophysics. This research on neutron-star physics should lead to more accurate methods of measuring the detailed properties of the extremely high-density material inside neutron stars. These results could have an impact on earth-based laboratory nuclear physics, in addition to its contribution to astrophysics. This project will also develop new computational methods for performing simulations of gravitational effects on the large-scale structure and evolution of the entire universe. These methods will provide advances in the field of computational mathematics. Some of these research projects are likely to involve undergraduate and graduate students, and will therefore contribute to the development of the next generation of scientists. New research will be conducted that will allow observations of neutron stars and our understanding of strong gravitational fields to be used to determine the neutron-star equation of state in a way that is free from any assumptions about the microphysics of neutron star matter. The projects include work in numerical relativity that involves developing techniques for solving Einstein's equations on manifolds with arbitrary spatial topologies. These methods will be used to study a variety of problems, including an effort to explore the gravitational analog of the turbulent cascade seen in fluid systems, and exploring cosmological models numerically to determine whether and how non-trivial topology could be recognized through observations. 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.