ÃÛÌÒTV

Abstract: Although solutions to Teukolsky’s radial equation play a key role in black hole perturbation theory, there are limitations in our understanding that obscure our practical use and application of e.g. quasi-normal mode overtone solutions. Towards addressing these limitations, I’ll present a collection of results: a radial scalar product for black hole quasi-normal modes, novel polynomials for quasi-normal mode radial functions, exact tridiagonalization of Teukolsky's radial equation, and spatial quasi-completeness of quasi-normal modes. I’ll conclude by discussing these findings in the context of old and new results in single black hole perturbation theory.