# Computational and astrophysical studies of black hole spacetimes

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This dissertation addresses three problems of interest concerning astrophysical black holes, namely the numerical solution of Einstein’s equations for a spacetime containing two orbiting and coalescing black holes, the simulation of a light curve from an accretion disk near the innermost orbit around a spinning black hole, and determining relations between central black hole mass and host galaxy properties in active galactic nuclei. I first address the problem of setting the initial conditions for the Cauchy formulation of general relativity. I present the solution of the constraint equations via a conformal decomposition and discuss the construction of the background fields as superposed Kerr-Schild black holes. The constraint equations are solved for two black holes with arbitrary linear and angular momenta. The binding energy and spin-spin coupling of the two holes are computed in the initial data slice and analyzed. I discuss the extent to which the superposed Kerr-Schild initial data limits extraneous radiation and estimate the accuracy of determinations of the innermost stable circular orbit through sequences of initial data. The second topic concerns the time variability of isotropically radiating material orbiting in an idealized accretion disk around a spinning black hole. I solve the geodesic equations for photon propagation from the surface of the disk to an observer for different orbital parameters. The general relativistic effects upon the signal received are calculated, including the energy shift, relativistic time delay, and gravitational lensing. I produce light curves showing the change in flux over time due to the relativistic effects. Applications of this model to stellar-mass systems as well as super-massive black holes are discussed. Lastly, I discuss the relationship between a galaxy’s central black hole and its evolutionary history. In particular I examine the correlations among host galaxy luminosity, stellar velocity dispersion, and central black hole mass in active galactic nuclei. I derive black hole masses and stellar velocity dispersions from quasar broad and narrow emission lines, respectively. The utility of using the narrow line emitting gas as a surrogate for stellar velocity dispersion is investigated through examining host magnitudes and narrow [O III] line widths for low redshift quasars.