New wrinkles on black hole perturbations: Numerical treatment of acoustic and gravitational waves

This thesis develops two main topics. A full relativistic calculation of quasinormal modes of an acoustic black hole is carried out. The acoustic black hole is formed by a perfect, inviscid, relativistic, ideal gas that is spherically accreting onto a Schwarzschild black hole.;The second major part is the calculation of sourceless vector (electromagnetic) and tensor (gravitational) covariant field evolution equations for perturbations on a Schwarzschild background using the relatively recent M2xS2 decomposition method. Scattering calculations are carried out in Schwarzschild coordinates for electromagnetic and gravitational cases as validation of the method and the derived equations.