We use a Monte Carlo code to calculate the geodesic orbits of test particles around Kerr black holes, generating a distribution function of both bound and unbound populations of dark matter particles. From this distribution function, we calculate annihilation rates and observable gamma-ray spectra for a few simple dark matter models. The features of these spectra are sensitive to the black hole spin, observer inclination, and detailed properties of the dark matter annihilation cross section and density profile. Confirming earlier analytic work, we find that for rapidly spinning black holes, the collisional Penrose process can reach efficiencies exceeding $600%$, leading to a high-energy tail in the annihilation spectrum. The high particle density and large proper volume of the region immediately surrounding the horizon ensures that the observed flux from these extreme events is non-negligible.
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