## Computational and astrophysical studies of black hole spacetimes

##### Abstract

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.

##### Department

##### Description

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