Fermion Quasi-normal modes of the Kerr Black-Hole

In this paper we study the fermion quasi-normal modes of a 4-dimensional rotating black-hole using the WKB(J) (to third and sixth order) and the AIM semi-analytic methods in the massless Dirac fermion sector. These semi-analytic approximations are computed in a pedagogical manner with comparisons made to the numerical values of the quasi-normal mode frequencies presented in the literature. It was found that The WKB(J) method and AIM show good agreement with direct numerical solutions for low values of the overtone number $n$ and angular quantum number l.