Extreme-mass-ratio inspirals: Waveform models and signal space

Extreme-mass-ratio inspirals (EMRIs) are the only gravitational-wave sources for the future LISA detector that combine the issue of strong-field complexity with that of long-lived signals. The result is a profoundly difficult inverse problem, with many theoretical and computational challenges presented both by the forward modeling of the predicted EMRI waveform, and by the recovery of an inverse solution for the presence and properties of actual EMRI signals in LISA data. I outline recent progress and ongoing work on both fronts. Specifically, I describe: i) the next generation of accurate, efficient and extensive models for (the response of LISA to) an EMRI signal; and ii) a heuristic study of degeneracy in the space of LISA-observable EMRIs, with a view to informing analysis strategies for EMRI search and characterization.