Non-local parameter degeneracy in the intrinsic space of gravitational-wave signals from extreme-mass-ratio inspirals

Extreme-mass-ratio inspirals will be prized sources for the upcoming space-based gravitational-wave observatory LISA. The hunt for these is beset by many open theoretical and computational problems in both source modeling and data analysis. We draw attention here to one of the most poorly understood: the phenomenon of non-local correlations in the space of extreme-mass-ratio-inspiral signals. Such correlations are ubiquitous in the continuum of possible signals (degeneracy), and severely hinder the search for actual signals in LISA data. However, they are unlikely to manifest in a realistic set of putative signals (confusion). We develop an inventory of new analysis tools in order to conduct an extensive qualitative study of degeneracy - its nature, causes, and implications. Previously proposed search strategies for extreme-mass-ratio inspirals are reviewed in the light of our results, and additional guidelines are suggested for the scientific analysis of such sources.