Post-Newtonian expansions of Kerr EMRIs: Equatorial-eccentric and spherically-inclined orbits*

With the Laser Interferometer Space Antenna (LISA) expected to launch in between the mid-to-late 2030s, extreme-mass-ratio inspirals (EMRIs) are receiving careful theoretical attention. We focus our attention on EMRIs with Kerr primaries. We examine these systems in the simultaneous extreme-mass-ratio and wide orbit limits, using first-order black hole perturbation theory and making post-Newtonian (PN) expansions of self-force quantities. We present analytic expressions of 1) gravitational fluxes in the case of a small mass in eccentric-equatorial motion up to 7PN and e²⁰ and 2) scalar fluxes in the case of a scalar-charged particle in a spherically-inclined orbit up to 8PN with no limits on inclination. We discuss the methods that are used to construct these analytic expressions and discuss the functional dependence of the fluxes on eccentricity and inclination, respectively. Additionally, we compare the PN expansions to full black hole perturbation numerical data, to examine the convergence of the PN expansions at close separations.