Dynamics of Black Holes and Dark Matter in Galactic Nuclei

This thesis presents theoretical studies of the dynamics of stars and stellar mass black holes around supermassive black holes. We additionally study the dynamics of dark matter in galaxy mergers. The first part of this thesis focuses on the observational signatures of cusps of stellar mass black holes that surround supermassive black holes. The second chapter shows that a cusp of stellar mass black holes in the galactic center can eject stars from the Milky Way galaxy with velocities up to \(\sim 2000\,{\rm km}\,{\rm s}^{-1}\). The rates we calculate are comparable to the tidal break-up of binary stars by the supermassive black hole. In the third chapter, we study how a mass spectrum of stellar black holes segregates around supermassive black holes. We find that the most massive black holes dominate the dynamics in the inner cusp. We also find a new source of gravitational waves: the formation and inspiral of black hole binaries that form owing to gravitational bremsstrahlung. We find that these eccentric mergers will be an interesting source to detect with future ground-based gravitational wave detectors. The fourth and fifth chapters look at the influence of gravitational wave recoil on merger of the first supermassive black holes to form in the centers of galaxies. We find that one inevitable consequence of gravitational wave recoil is the ejection of hundreds of black holes into the Milky Way halo. We show that these black holes are surrounded by a cluster of stars that can be used to search for the black holes. In the fourth chapter, we follow the long term evolution of these stellar systems, and search for them in the Sloan Digital Sky Survey. The sixth chapter describes our work on the dynamics of dark matter in galaxy mergers. We focus on the interaction between the dense baryonic bulges that exist in the centers of galaxy and the dark matter that surrounds them. We find that the baryons protect the dark matter during mergers, and maintain steep density cusps if they form with a cusp of dark matter. However, the bulges can also eject dark matter on scales many times their radii