Black holes and accretion disks in active galactic nuclei: Microlensing, caustics, and collisional stellar dynamics

Interactions between and the structure of black holes, accretion disks, and dense star clusters are investigated. Observed rapid gravitational microlensing variability in the quasar Q2237+0305 is used in conjunction with numerical simulations to determine whether the observations constrain theoretical accretion disk models. It is found that blackbody disks are too large to account for the observed variability, and it is argued that the optical emission is either nonthermal or optically thin.; Accurate and efficient routines to compute geodesic trajectories in the Kerr spacetime describing rotating black holes are implemented and applied to several problems. The optical caustic structure of the Kerr metric describing rotating black holes is determined and its possible relevance to rapid X-ray variability in active galactic nuclei is discussed. Sample point source light curves and the appearance of thick accretion disks around Kerr black holes are calculated and the influence of caustics on them is assessed.; The dynamical evolution of the core of a dense star cluster around a Kerr black hole and under the influence of star-disk interactions is examined. It is shown that there are astrophysically plausible regimes in which star-disk interactions can dominate all other dynamical processes. The effects of star-disk interactions on single orbits are illustrated. It is found that star-disk interactions steepen the initial density profile towards an equilibrium r{dollar}sp{lcub}-3{rcub}{dollar} profile and increase the central density by up to two orders of magnitude. It is argued that this process could self-limit when densities climb to such a level that collisions between stars become important.; Simulations of the dynamical evolution of the density cusp of a star cluster around a massive black hole in a regime where stellar collisions dominate other dynamical processes are performed. The calculations are done using discrete stars and a fully relativistic formalism. Versatile numerical methods are developed and applied to this problem. A modified form of Kepler's Equation asymptotically valid in the Kerr geometry is derived. It is found that collisions produce a constant density core populated by stars in highly radial orbits. Collisional refilling of the loss cone is seen. Additional applications of the numerical algorithms are suggested.