Exact solutions of the angular Teukolsky equation for particular cases

Abstract

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 0Al0≈[l(l+1)-τR2/2]-iτI2/2 with an arbitrary τ2=τR2+iτI2. The angular probability distribution (APD) for the ground state moves towards the north and south poles for τR2>0, but aggregates to the equator for τR2≤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.

Keywords

• Angular Teukolsky equation
• Exact solutions
• Confluent Heun equation