Exact solutions of the angular Teukolsky equation for particular cases

In this work we solve the angular Teukolsky equation in alternative way for a more general case τ≠0 but m=0,s=0. We first transform this equation to a confluent Heun differential equation and then construct the Wronskian determinant to calculate the eigenvalues and normalized eigenfunctions. We find that the eigenvalues for larger l are approximately given by 0A_l0≈[l(l+1)-τ_R²/2]-iτ_I²/2 with an arbitrary τ²=τ_R²+iτ_I². The angular probability distribution (APD) for the ground state moves towards the north and south poles for τ_R²>0, but aggregates to the equator for τ_R²≤0. However, we also notice that the APD for large angular momentum l always moves towards the north and south poles, regardless of the choice of τ².