A solution method determining the effect of spin upon gravitational effects in the surroundings of a black hole

Using the theory of General Relativity and quasi-normal modes (QNMs) from the Teukolsky equation as a source of quasi-periodic oscillations (QPOs) from black holes provides information about black hole mass and spin. This is related to standing wave resonance phenomena of gravitons and photons trapped in a gravitational potential well surrounding the black hole and provides evidence for the existence of standing wave gravitons in a high gravitational environment , which are observable by the QPO frequencies as infalling electrons interact with these resonance states. We calculate the QNM angular frequency as a function of spin parameter and create regression equations to relate these frequencies back to spin parameter. The QNM frequencies are what can be experimentally measured , and therefore are preferred as the independent variables. We then compare these equations to QPO data collected from the supermassive black hole Sgr A* and stellar mass black hole GRS1915+105 to calculate the spin parameter for each. The spin parameter of Sgr A* is calculated to be 0.431 plus or minus 0.075 and the spin parameter for GRS1915+105 is calculated to be -0.9875 plus or minus 0.0005. This indicates GRS1915+105 has a retrograde spin. Due to the precise measurement of the QPOs from GRS1915+105 , we are able to calculate the mass of the black hole to be 10.09 Solar Masses using the necessity for consistency of mass and spin between the graviton and photon resonances