Online

Myhaver, Vanessa

Complex Systems and Data Science

2022

M.S.

Extreme--mass--ratio inspirals (EMRI) are prospective sources for the detection of observational signals with the Laser Interferometer Space Antenna (LISA) mission, built to accurately detect and measure gravitational waves -- ripples in the curvature, and fabric of space--time. EMRIs are typically comprised of a supermassive black hole (SMBH) one million times more massive than our Sun, and a stellar--origin black hole several orders of magnitude smaller. As the smaller black hole spirals into the supermassive black hole, thousands of cycles of the gravitational waveform serve as a precision probe for the extreme space-time curvature of the system. The goal of this research is to model the dynamics of and calculate the gravitational waveforms from ``Trojan analog'' EMRIs: multiple EMRIs in a single system, locked in 1:1 resonant orbits, analogous to Jupiter's Trojan asteroids. In this thesis, we present and confirm the accuracy of the methods used to calculate the equations of motion of such a system using Newtonian, 1st post-Newtonian (PN), and 2.5 PN terms of motion with Hamiltonian Mechanics. Using the resulting motion of the three--body system, we present methods used to calculate the gravitational waves produced by the system's inspiral using the quadrupole formula. We then conduct a comparison test of the Resonant Trojan system to a Single, classical EMRI system which concludes that these Trojan EMRIs hold a mix of unique observational potentials, distinct from those of Single EMRI systems, that may be detectable with the LISA mission, while simultaneously providing detailed orbital dynamics around a supermassive black hole.