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Abstract

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.