  While Albert Einstein's theory of General Relativity (GR) has been tested
extensively in our solar system, it is just beginning to be tested in the
strong gravitational fields that surround black holes. As a way to study the
behavior of gravity in these extreme environments I have used and added to a
ray-tracing code that simulates the X-ray emission from the accretion disks
surrounding black holes. In particular, the observational channels which can be
simulated include the thermal and reflected spectra, polarization, and
reverberation signatures. These calculations can be performed assuming GR as
well as four alternative spacetimes. These results can be used to see if it is
possible to determine if observations can test the No-Hair theorem of GR which
states that stationary, astrophysical black holes are only described by their
mass and spin. Although it proves difficult to distinguish between theories of
gravity it is possible to exclude a large portion of the possible deviations
from GR using observations of rapidly spinning stellar mass black holes such as
Cygnus X-1. The ray-tracing simulations can furthermore be used to study the
inner regions of black hole accretion flows. I examined the dependence of X-ray
reverberation observations on the ionization of the disk photosphere. My
results show that X-ray reverberation and X-ray polarization provides a
powerful tool to constrain the geometry of accretion disks which are too small
to be imaged directly. The second part of my thesis describes the work on the
balloon-borne X-Calibur hard X-ray polarimetry mission and on the space-borne
PolSTAR polarimeter concept.
