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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.

Using Simulations of Black Holes to Study General Relativity and the Properties of Inner Accretion Flow