Analytical expansions of eccentric-equatorial and inclined-spherical Kerr EMRIs: pushing to 10PN relative order

With the Laser Interferometer Space Antenna (LISA) anticipated to launch in the mid-2030s, expected targets are coming under heavier scrutiny. Among these are extreme-mass-ratio inspirals (EMRIs). Working in the simultaneous extreme-mass-ratio and wide-orbit regime, we examine EMRIs with a Kerr primary using black hole perturbation theory and then taking a post-Newtonian expansion of self-force quantities. We show analytical expressions expanded to 10PN relative order for two types of EMRIs. In the first case, we consider eccentric-equatorial orbits on a Kerr primary, making not only a PN expansion but also an expansion in eccentricity up to e²⁰. Secondly, we consider inclined-spherical orbits on a Kerr primary for arbitrary inclination. The analytical PN (and eccentricity) expansions are then compared to numerical data generated by full Teukolsky codes to examine the convergence as one pushes towards close separation, high inclination and high eccentricity.