Recent observations have shown that about 70% of the energy density in the universe cannot be attributed to matter. The simplest explanation of this `dark energy' comes from the cosmological constant that Einstein had initially introduced in his fundamental equations of general relativity. However, for most of the 20th century, it was widely believed that the cosmological constant is zero because all observations were compatible with this simplest possibility. Therefore, the detailed mathematical theories describing the dynamics of compact astronomical objects such as colliding black holes and neutron stars, and gravitational waves they source, was based on this assumption. The goal of the first part of this project is to systematically extend that theory to include a non-zero cosmological constant. The extension will provide a firmer foundation for gravitational wave science. The second part of the project contains studies at the interface of strong gravity and quantum physics. They address fundamental issues related to the quantum evaporation of black holes and the physics of the earliest epoch of our universe when gravity is strong and quantum physics indispensable. The proposed research will have an impact on a broad range of research areas, including general relativity, geometric analysis, cosmology, quantum field theory, and computational science. As a result, through this research, young scientists will be trained in inter-disciplinary science. Currently, these researchers include members of under-represented groups. Through his editorship of series commemorating the centennial of the discovery of general relativity, the PI will commission monographs aimed at communicating the latest advances in science and technology to young researchers. Finally, as in the past, personnel supported by this grant will contribute vigorously to outreach activities through videos, semi-popular articles and public lectures.
The first part of the project will address issues arising from the fact that even a tiniest value if the cosmological constant can cast a long shadow on the theory of gravitational waves. As of now, we do not even have a gauge invariant notion of gravitational waves in full, non-linear general relativity with a positive cosmological constant. The goal is to construct a rigorous framework to fill this gap and use it to extract the physics of gravitational waves in a more reliable fashion. The results will open new avenues for analytic and numerical work in the study of the gravitational collapse, compact binary coalescence, energy, momentum and angular momentum emission in such processes, post-Newtonian and post-Minkowskian approximation methods, etc. They are also likely to stimulate research in geometric analysis through new mathematical conjectures (related to positivity of a new notion of energy). The second part of the project will address two types of issues: i) the conceptually fundamental question of whether information is lost in evaporation of black holes; and, ii) the emerging interplay between loop quantum gravity and observations related to the very early universe. This is possible because loop quantum cosmology is now sufficiently mature to make predictions for future observations based on its pre-inflationary dynamics, and to use current observations to seek fundamental principles that presumably dictate the initial conditions for our universe.
|Effective start/end date||8/1/15 → 7/31/18|
- National Science Foundation: $1,015,710.00