Description
In this research the vector space properties of the solution space to the radial Teukolsky equation for Kerr and Schwarzschild Black Hole (SBH) QuasiNormal Modes (QNM) will be discussed. More specifically the properties of Confluent Heun Functions will be used in order to understand if it is possible to construct an orthonormal basis for the solution space of the radial Teukolsky equation obeying QNM boundary conditions. This poster constructs an extensive and detailed overview of which frequencies are quasinormal modes and which are not, including limiting cases. The poster points out several modes lacking or wrongly included in the literature. One finds, for the first time (to the best of the author’s knowledge), preliminary evidence regarding the overcompleteness of QNM radial wavefunctions of SBHs using explicitly a bilinear form. A set of adjoint radial wavefunctions is constructed which orthonormalizes the vector space. This orthonormal set is a new step towards a projection operator for QNMs. Further studies should formalize this framework, test these results and should extend this study to near extremal black holes, which may lead to new subtleties.
