Dynamics of General Extreme Mass Ratio Inspiral Resonances

Extreme mass ratio inspirals (EMRIs) are scenarios in which a smaller body spirals into a black hole at least ten thousand times more massive. When the Laser Interferometer Space Antenna (LISA) launches, it will be able to pick up the gravitational waves (GWs) coming from EMRI events where the larger body is a supermassive black hole (SMBH) [1], such as in the galactic center. However, said galactic centers are crowded, leading to perturbations of the EMRI system and, therefore, changing their emitted GWs [2]. The most significant change comes when an object further out from the inspiral enters into a resonance with the smaller EMRI body [2]. Our goal with this project is to develop a method of quantifying the effects of the resonance on the inner body's orbit and classifying the types of resonance encounters for any set of possible orbits, expanding on prior research to generalize to non-circular orbits [3]. We do this by simulating potential orbits for both objects, identifying resonance encounters, and then determining whether the resonance is a crossing or a capture. The method is able to find resonance encounters across the entire evolution of the EMRI system and categorize the type of resonance at each encounter. The proper identification of resonances can be used to describe the dynamics near galactic centers we observe and to distinguish perturbations caused by resonances from perturbations caused by deviations from general relativity [4].