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Event details

Title: Numerical approaches to first- and second-order self-force calculations

Abstract: Extreme-mass-ratio inspirals (EMRIs) - binary systems wherein a small compact object inspirals into a supermassive black hole - are considered to be important potential sources for the future space-based gravitational wave detector LISA. Inspirals of this nature are long-lived and are expected to possess a highly complex morphology with eccentric and precessing trajectories of the small compact object. Therefore, systems of this nature are unique in the parameter space since they offer an unparalleled insight into the strong-field regime of general relativity through radiated gravitational waves (GWs). Achieving this scientific insight will require highly accurate waveform templates that remain phase accurate over these long inspirals. The characteristic small-ratio and stringent accuracy requirements make second-order self-force theory indispensable. A principal challenge at second-order is the construction of the source term in the field equations. Unlike at first order, the second-order source is unbounded and involves coupled singular and regular contributions that must be carefully separated and regularised. Maintaining long-term phase accuracy further requires a multiscale expansion of the field equations to capture slow-time inspiral effects, introducing additional structural complexity. In this talk, I will review the current state of second-order gravitational self-force (GSF) theory and present recent advances in extending these calculations to spinning primaries. In particular, I will describe progress on constructing the second-order source term in Kerr spacetime and new computational strategies for solving the field equations up to non-linear order.