Gas near the center of a galaxy can find its way into the central black hole without much difficulty, but stars need to be nudged. The so-called "loss-cone problem" is well understood in the case of random gravitational encounters between the stars. But sufficiently close to a nuclear black hole, classical loss-cone theory breaks down, for two reasons: the orbits are quasi-Keplerian, and so maintain their orientations for many periods, violating the assumption of randomness; and general relativity begins to become important. These new effects are relatively unimportant for the rate of consumption of normal stars. But compact objects -- neutron stars and stellar-mass black holes -- can survive much closer to the central black hole where these effects dominate the collective evolution. I will present new results, based on a variety of methods (N-body, test-particle, Fokker-Planck) for simulating the long-term evolution of nuclear star clusters in this near-field regime. The results are relevant to the "EMRI" (extreme-mass-ratio inspiral) problem, and also to the rate at which compact objects interact with each other near the centers of galaxies.
Followed by wine and cheese in Pupin 1402.