Simulation and Study of Extreme Mass Ratio Inspirals and Gravitational Waveforms

Since its confirmed direct detection in 2015, gravitational radiation has become a promising addition to the toolbox of multi-messenger astronomy, alongside more established messenger signals such as neutrinos, cosmic rays, and electromagnetic radiation. By continuing to develop our understanding of the phenomenon, it is possible to obtain a more thorough comprehension of objects and events outside our solar system, and potentially even allow us to gather data on events that are not observable via the other messengers. To that end, the number of currently existing and planned gravitational wave observatories has only grown in the last decade, up to and including the Laser Interferometer Space Antenna (LISA), an ESA-led space-based observatory with a planned launch in the 2030s. LISA will be sensitive to a range of frequencies unavailable to current detection methods, lower than what ground-based observatories such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States and the Virgo Interferometer in Italy can detect, but higher than the viable range for pulsar timing arrays like the European Pulsar Timing Array (EPTA) or the North American Nanohertz Observatory for Gravitational Waves, making it an ideal method of observing a larger range of gravitational wave sources, including Extreme Mass Ratio Inspirals (EMRIs), a type of pairing between compact stellar-mass objects and supermassive black holes that lead to the eventual capture of the smaller body. EMRIs are expected to be reasonably common, relatively nearby, provide an excellent test of general relativity in the strong gravity regime, and serve as a completely new tool to probe the environments of galactic nuclei. In order to categorize and interpret the data from next-generation observatories like LISA effectively, it is essential to prepare useful data analysis methods and techniques before they become necessary. In this work, we develop a small but robust toolbox of these techniques, designed to serve as a reliable groundwork for more targeted methods in the near future.