Direct numerical integrations of the two-dimensional Fokker-Planck equation are carried out for compact objects orbiting a supermassive black hole (SBH) at the center of a galaxy. As in Papers I-III, the diffusion coefficients incorporate the effects of the lowest-order post-Newtonian corrections to the equations of motion. In addition, terms describing the loss of orbital energy and angular momentum due to the 5/2-order post-Newtonian terms are included. In the steady state, captures are found to occur in two regimes that are clearly differentiated in terms of energy, or semimajor axis; these two regimes are naturally characterized as plunges (low binding energy) and EMRIs, or extreme-mass-ratio inspirals (high binding energy). The capture rate, and the distribution of orbital elements of the captured objects, are presented for two steady-state models based on the Milky Way: one with a relatively high density of remnants and one with a lower density. In both models, but particularly in the second, the steady-state energy distribution and the distribution of orbital elements of the captured objects are substantially different than if the Bahcall-Wolf energy distribution were assumed. The ability of classical relaxation to soften the blocking effects of the Schwarzschild barrier is quantified.These results, together with those of Papers I-III, suggest that a Fokker-Planck description can adequately represent the dynamics of collisional loss cones in the relativistic regime.
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