Fake plunges are very eccentric real EMRIs in disguise ... they dominate the rates and are blissfully ignorant of angular momentum barriers

The capture of a compact object in a galactic nucleus by a massive black hole (MBH) is the best way to map space and time around it. Compact objects such as stellar black holes on a capture orbit with a very high eccentricity have been wrongly assumed to be lost for the system after an intense burst of radiation, which has been described as a "direct plunge". We prove that these very eccentric capture orbits spend actually a similar number of cycles in a LISA-like detector as those with lower eccentricities if the central MBH is spinning. Although the rates are higher for high-eccentricity EMRIs, the spin also enhances the rates of lower-eccentricity EMRIs. This last kind have received more attention because of the fact that high-eccentricity EMRIs were thought to be direct plunges and thus negligible. On the other hand, recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on these lower-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statitical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian but also, and for the first time, a geodesic approximation for the relativistic orbits. The existence of the barrier prevents "traditional EMRIs" from approaching the central MBH, but if the central MBH is spinning the rate will be anyway dominated by highly-eccentric extreme-mass ratio inspirals, which insolently ignore the presence of the barrier, because they are driven by two-body relaxation.