This award supports theoretical research on strongly gravitating systems, such as black holes and neutron stars. These objects push the known laws of physics to their limits, offering opportunities for advancing fundamental understanding. The goal is to study novel gravitational phenomena and determine how they can be observed, both in principle and in practice. Examples include signatures of strong light-bending near black holes, as observed with Event Horizon Telescope and successors, and the role of conservation laws in the dynamics of two-body interactions in general relativity, as observed with gravitational waves. This will allow rigorous tests of fundamental law and provide opportunities for new discoveries. The results will be communicated to the public on social media. The specific projects are divided up into two categories: signatures of orbiting light, and compact object interactions. Orbiting light imprints a "photon ring" on black hole images, which carries detailed information about the underlying spacetime. Novel photon ring observables will be studied and their ability to test gravity will be quantified. Compact object interactions pose theoretical challenges related to the long-range nature of the gravitational force, and a mathematically complete description requires consideration of the full Bondi-Metzner-Sachs (BMS) asymptotic symmetry group of asymptotically flat spacetimes in general relativity. This approach will be used to resolve puzzles about angular momentum that have arisen in perturbative calculations and to provide a framework for comparing the results of different calculations and/or experimental results. 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.