On modeling for Kerr black holes: basis learning, QNM frequencies, and spherical-spheroidal mixing coefficients

Models of black hole (BH) properties play an important role in the ongoing direct detection of gravitational waves from BH binaries. One important aspect of model based gravitational wave (GW) detection, and subsequent estimation of source parameters, is the low level modeling of information related to perturbed Kerr black holes. Here, we present new phenomenological methods to model the analytically understood GW spectra (quasi-normal mode frequencies), and harmonic structure of Kerr black holes (mixing coefficients between spherical and spheroidal harmonics). In particular, we present a greedy-multivariate-polynomial (GMVP) regression method and greedy-multivariate-rational (GMVR) regression method for the automated modeling of polynomial and rational functions, respectively. GMVP is used to develop a model for QNM frequencies that explicitly enforces consistency with the extremal Kerr limit. GMVR is used to develop a model for harmonic mixing coefficients for the dominant multipoles with . The models for the mixing coefficients are the first of their kind to consider BH spin to vary between???1 and 1, thus naturally connecting the pro and retrograde modes. We discuss the potential use of these models in current and future GW signal modeling.