Determining the Asymptotic Expansion of Prolate Spin-Weighted Spheroidal Eigenvalues

Spin-Weighted Spheroidal Harmonics (SWSHs) are a complete orthonormal basis of tensors on the surface of spheroids. While SWSHs are used in many fields of physics for modeling, this research is focused on their application to describing the normal modes of transmission on the surface of black holes in the Kerr Geometry. Much is known for the oblate case of SWSHs; however, the asymptotic behavior of the prolate case has yet to be well described. In this work, the prolate SWSHs problem was numerically solved, which was used to create a power series approximation for their eigenvalues.