From Equal-mass to Extreme-mass-ratio Binary Inspirals: Simulation Tools for Next Generation Gravitational Wave Detectors

Current numerical codes can successfully evolve similar-mass binary black holes systems, and these numerical waveforms contributed to the success of the LIGO Collaboration\u27s detection of gravitational waves. LIGO requires high resolution numerical waveforms for detection and parameter estimation of the source. Great effort was expended over several decades to produce the numerical methods used today. However, future detectors will require further improvements to numerical techniques to take full advantage of their detection capabilities. For example, the Laser Interferometer Space Antenna (LISA) will require higher resolution simulations of similar-mass-ratio systems than LIGO. LISA will also be able to detect extreme-mass-ratio inspiral (EMRI) systems. The EMRIs require a perturbative approach, and these techniques lags far behind numerical relativity. Improvements to current similar-mass codes and development of EMRI codes are necessary for future gravitational wave studies. My first project improved the underlying framework of the Einstein Toolkit (ETK). I improved the ETK by implementing a new method for scheduling ghost zone synchronization and application of boundary conditions. The new approach reduces inter-processor communication overhead and improves the user experience. These improvements to the ETK improve its computational efficiency and enable users to more easily contribute to the collaboration. I also implemented the first-order perturbative evolution equations for the EMRI system. This work builds on code for simulating the toy model of a particle with a scalar charge. This code differs from other time domain codes by evolving self-consistently by using the full self-force to provide a highly accurate waveform. I extended this code to be capable of evolving gravitational fields. I implemented even and odd master functions for the Regge-Wheeler-Zerilli gauge and verified convergence of the energy and angular momentum fluxes to frequency domain results. I derived and implemented evolution equations in the Lorenz gauge. The evolution equations in the Lorenz gauge are considerably more complicated than the Regge-Wheeler-Zerilli gauge, and my code currently does not match the expected results. Still, my code is stable at long times and has effective constraint damping. These two codes represent significant progress towards the self-consistent evolution of the EMRI system at first order