RUI: Investigating Gravitational Waves and Extreme Mass-Ratio Compact Binaries

This award supports theoretical investigations of the gravitational waves (GWs) emitted when a stellar mass compact object, such as a neutron star or black hole, inspirals into a supermassive black hole. These extreme mass-ratio inspirals (EMRIs) are important astronomical sources of GWs that will be observed by the upcoming Laser Interferometer Space Antenna (LISA) detector, which is under cooperative development by NASA and the European Space Agency. This project involves pursuit of a new approach to mathematical modeling that is able to achieve improved realism in a way that avoids technical hindrances encountered in prior work. Accurate EMRI models implemented through this award will enable LISA observations to reveal the inner workings of gravitational interactions like never before. This work involves direct training of quantitative technical skills for undergraduate student researchers, which are highly transferable to STEM related careers in other sectors. This award supports a synergistic physics education research project that will simultaneously improve upper-level undergraduate physics instruction and provide a testing ground to research new mathematical modeling techniques. The research objective of this award is to determine how relativistic two-body interactions influence the dynamics of EMRIs utilizing a new approach to self-force (SF) calculations recently discovered by the PI’s research group. Two-body interactions governing EMRIs are accurately dissected by applying black hole perturbation theory (BHPT) to expand the gravitational field and associated SF exerted on the secondary body up to an appropriate order in powers of the small mass-ratio. The new approach pursued by this project involves computation of Kerr metric perturbations by solving elliptic partial differential equations (PDEs), which avoids previously encountered numerical instabilities in Lorenz gauge self-force calculations. Those instabilities are avoided by entering the frequency domain, where the field equations involve only r and theta derivatives and are solved numerically. This project will research and implement the novel elliptic PDE SF method to calculate the 1st order Lorenz gauge Kerr gravitational SF, which opens a pathway to begin exploring the needed 2nd-order Kerr SF. Completion of this project will enhance fundamental understanding of gravitational physics and EMRI dynamics in ways that will assist GW data analysis and reveal the foundations of strong-field gravity with unprecedented precision. 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.