Dirac equation in Kerr geometry and its solution

Abstract

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. In the present review, we present solutions of the complete wave equation and discuss how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed for different Kerr parameters. We compare the solutions with several parameters to show how a spinning black hole distinguishes mass and energy of incoming waves. Very close to the horizon, the solutions become independent of the particle parameters indicating an universality of the behaviour.