Novel 3D visual comparisons between the spherical harmonics and Kerr spheroidal harmonics

Black holes are natural outcomes of the theory of general relativity and are subjects of wide interest for physicists and astronomers. The Teukolsky equation describes linear perturbations of a rotating Kerr black hole and applies to various massless fields, including gravitational, electromagnetic, scalar, and neutrino fields. This equation is applied to study phenomena such as gravitational waves resulting from the mergers of two black holes and other properties, including their quasinormal modes. In this talk, we present a fully numerical approach to better understand the solutions of the angular Teukolsky equation by utilizing the spherical-spheroidal spectral decomposition method. The novelty of our study lies in the case-by-case visual comparison between the spherical harmonics Y_lm(θ,φ)  and Kerr spheroidal harmonics S_lm(θ,φ;aω) for a wide range of values of the oblateness parameter aω. We generate new 3D visuals for S_lm(θ,φ;aω) and compare them with the existing 3D visuals of Y_lm(θ,φ). We believe our result adds one more tool to better understand the effect of the rotation of a black hole on deforming the usual spherical harmonics for rotating black holes.