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

Abstract

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.