OBSERVATIONS OF ACCRETION IN BLACK HOLE CANDIDATE X-RAY BINARIES AND ULTRALUMINOUS X-RAY SOURCES HAVE REACHED A POINT WHERE THEY ARE CAPABLE OF PROVIDING TIGHT CONSTRAINTS ON THE PROPERTIES OF THE ACCRETION FLOWS AND THE BLACK HOLE SPACETIMES IN WHICH THEY RESIDE. AT THIS POINT A PRIMARY LIMITATION IS THE QUALITY OF THE MODELS USED TO INTERPRET THE DATA. IN ORDER TO PROVIDE BETTER FIRST-PRINCIPLES MODELS WE PROPOSE TO EXTEND THE CAPABILITIES OF OUR RADIATION HYDRODYNAMICS CODE TO INCLUDE MONTE CARLO BASED RADIATION TRANSFER METHODS. THIS EXTENSION WILL ALLOW US TO BETTER CAPTURE THE FREQUENCY DEPENDENT ASPECTS OF THE RADIATIVE TRANSFER PROBLEMS IN OUR SIMULATIONS AND TO PROVIDE DETAILED SIMULATION BASED PREDICTIONS OF THE SPECTRUM VARIABILITY AND POLARIZATION OF BLACK HOLE ACCRETION FLOWS. WE HAVE ALREADY DEVELOPED STATE-OF-THE-ART RADIATION TRANSFER ALGORITHMS FOR SOLVING THE ANGLE DEPENDENT TRANSFER IN THE GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC CODE: ATHENA++. THESE RADIATION TRANSFER METHODS ALLOW US TO COMPUTE THE RADIATION FORCES HEATING AND COOLING SOURCE TERMS IN SIMULATIONS OF ACCRETION FLOWS. THE METHODS HAVE ALREADY BEEN IMPLEMENTED IN A SPECIAL RELATIVISTIC APPROACH AND WE ARE IN THE PROCESS OF EXTENDING THE RADIATION TRANSFER TO FULLY GENERAL RELATIVISTIC ALGORITHMS. THE RADIATION TRANSFER IS SOLVED IN THE SIMULATIONS USING A GRAY (FREQUENCY AVERAGED) CONSERVATIVE FINITE DIFFERENCE SCHEME. THIS APPROACH DOES NOT PROVIDE US WITH THE FREQUENCY DEPENDENT INFORMATION REQUIRED TO MAKE DETAILED SPECTRAL PREDICTIONS. THEREFORE WE PROPOSED TO DEVELOP A MONTE CARLO BASED ALGORITHM FOR SOLVING THE FREQUENCY DEPENDENT RADIATION TRANSFER EQUATION ON HYDRODYNAMICS SIMULATION GRID. IN THE FIRST STAGE OF THE PROJECT WE WILL INTEGRATE AND THE PIS EXISTING MONTE CARLO CODE INTO ATHENA ++ AND USE IT TO COMPUTE STEADY STATE SPECTRA FROM SNAPSHOTS OF TIME DEPENDENT SIMULATIONS. NEXT WE WILL EXTEND THE MODULE TO RUN IN CONCERT WITH THE SIMULATIONS TO PROVIDE TIME-DEPENDENT SPECTRAL PREDICTIONS. FINALLY WE WILL COUPLE OUR MONTE CARLO TRANSFER SCHEME DIRECTLY WITH THE HYDRODYNAMICS. WE WILL IMPLEMENT BOTH A MONTE CARLO ONLY FRAMEWORK AS WELL AS A HYBRID FRAMEWORK THAT COUPLES THE MONTE CARLO SOLVER TO A CONSERVATIVE FINITE DIFFERENCE INTEGRATOR OF THE RELATIVISTIC STRESS-ENERGY TENSOR IN BLACK HOLE SPACETIMES. THE PRIMARY GOALS OF THIS PROPOSAL ARE TO IMPROVE THE SIMULATIONS BY BETTER MODELING THE FREQUENCY DEPENDENT PROPERTIES OF THE RADIATION AND TO GENERATE DETAILED SPECTRAL PREDICTIONS. THE FIRST GOAL IS PARTICULARLY IMPORTANT FOR ACCURATELY MODELING THE HEATING AND COOLING EFFECTS DUE TO COMPTON SCATTERING WHICH CAN DEPEND SENSITIVELY ON THE LOCAL RADIATION SPECTRUM. THE SECOND GOAL ALLOWS US TO CONSTRUCT SOPHISTICATED SYNTHETIC SPECTRA WHICH CAN BE DIRECTLY COMPARED WITH DATA. WE WILL CREATE SIMULATED OBSERVATIONS USING THESE OUTPUTS AND ANALYZE THEM USING STANDARD SPECTRAL ANALYSIS SOFTWARE AND TECHNIQUES (E.G. XSPEC). THE RESULTS OF THIS ANALYSIS WILL AID IN INTERPRETING THE RESULTS FROM OBSERVATIONS WITH CURRENT AND FORMER X-RAY SATELLITES SUCH AS CHANDRA SWIFT NUSTAR XMM-NEWTON SUZAKU AS WELL AS FUTURE NASA MISSIONS SUCH AS IXPE AND XARM.