Computational investigation into Black Hole Quasi-normal modes of various systems

Investigation into the quantized excitations of linear fields in spacetime around a black hole provides further insight into black hole properties. One type of excitation to consider are quasi-normal modes, which are the energy eigenstates of the linear field around the black hole found from quantum mechanical analysis of the system. An example of quasi-normal modes can be found in the eigenstates of a scalar field around a Schwarzschild black hole. With the use of finite differencing adapted to nonlinear eigenvalue problems, we can perform this quantum mechanical analysis for other systems that are like the scalar field approximation. Quasi-normal modes of a system typically have dissipative properties due to energy loss into the event horizon. By performing this analysis, variation of quasi-normal modes from system to system can be found to evaluate how different cases affect the dissipation of energy around the black hole.