Relativistic Gravitation and Astrophysics

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The recent detections of gravitational waves by NSF's LIGO observatories and by astronomers of the motions of stars and gas near supermassive black holes, such as the one at the center of the Milky Way, have opened the possibility of testing Einstein's theory in realms where the warping of spacetime is extreme. Yet in order to test Einstein's great theory, it is essential to know what it actually predicts for real measurements. This project continues a program of research to provide concrete links between the abstract beauty and complex mathematics of Einstein's theory and the real world where measurements are made by physicists and astronomers. These links are established by finding approximate, yet accurate solutions of the equations in forms that are practical and usable. The outcomes of this research will be used by data experts at the gravitational-wave observatories to perform better tests of general relativity using newly detected signals, and will be used by astronomers to probe how general relativity affects complex systems such as stars orbiting supermassive black holes, or three-body systems involving bodies ranging from black holes to exoplanets. Einstein's theory is a topic that fascinates the general public, and the PI will continue to give public lectures on topics related to this research, bringing understanding of Einstein's ideas to the broader community.Specifically, this project will contribute to the ability of ground-based gravitational-wave observatories such as the LIGO-Virgo network to test general relativity, by computing the equations of motion for binary star systems, along with the emitted gravitational waveforms, as predicted by an important alternative theory, known as Einstein-Aether gravity, to high accuracy in the so-called post-Newtonian approximation. It will provide accurate waveforms predicted by this theory in a format that can be adapted to LIGO-Virgo data analysis methods. Another important question that will be addressed is whether the evolution of binary orbits with general relativistic effects included leaves any residual orbital ellipticity in the final stages, leading to observable modulations of the gravitational signals emitted. The project also extends recent work of the PI on incorporating the effects of Einstein's theory into the dynamics of three-body systems, such as a star-exoplanet system in the presence of a third body, or a binary-black-hole system in a galactic core with a supermassive black hole at its center.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.