| We develop physical models to describe the dynamics of N black holes inside dense stellar systems. For N = 1, we show that the force on a single massive black hole consists of two independent parts: the slowly varying influence of the aggregate stellar system, and a rapidly fluctuating stochastic force arising from discrete encounters with individual stars. Detailed properties of the resulting Brownian wandering of the black hole are calculated, and it is shown that in equilibrium, the position and velocity of the black hole are distributed as independent Gaussians. The results are applied to derive a lower limit on the mass of the black hole Sgr A* at the center of our Galaxy. We also consider whether in the stationary state the black hole achieves a state of equipartition of kinetic energy with the surrounding stars, and show that in certain cases, deviation from equipartition can be large.; For N = 2, we study the case of massive binary black holes in spherically symmetric bulges of galaxies, and investigate whether the Brownian motion of a binary's center of mass can allow its continued interaction with stellar orbits, and to keep hardening to the point of coalescence by the emission of gravitational radiation. We find that a considerable fraction of binaries in galaxies can by this means coalesce within a Hubble time. The predictions of the above models are confirmed by N-body simulations.; We examine the interactions of N 2 stellar-mass black holes in globular clusters with a population of primordial stellar binaries. We find that close encounters between them result in the rapid exchange of the stellar members of the binaries with black holes. Repeated encounters between the black hole binaries and single black holes then result in the ejection of almost all the black holes from the cluster in a fraction of the age of the Universe. This may explain why no accreting black holes in X-ray binaries have been seen in globular clusters. |
