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Explore advanced computational methods for modeling gravitational waves from extreme mass-ratio inspiral binary systems in this specialized physics lecture. Learn how hyperboloidal foliations can be combined with frequency-domain Teukolsky equations to compute gravitational self-force effects for eccentric equatorial orbits in Kerr spacetime. Discover the implementation of Fourier-domain worldtube puncture schemes that decompose black hole motion into radial and azimuthal modes, and understand how hyperboloidal compactifications regularize these modes to extract clean waveforms at null infinity. Examine the transition from spherically symmetric configurations to axially symmetric Kerr spacetimes, moving beyond the limitations of quasi-circular, equatorial orbits. Gain insights into the numerical structures used for equatorial motion modeling and explore potential generalizations to precessing and inclined orbits. Understand the significance of this work for future space-based gravitational wave observatories and its role in providing scalable pathways for accurate waveform modeling in extreme mass-ratio inspiral systems.
