Dirac equation in Kerr space-time

Abstract

The weak-field low-velocity approximation of the Dirac equation in Kerr space-time is investigated. The interaction terms admit an interpretation in terms of a 'dipole-dipole' interaction in addition to spin coupling with the angular momentum of the rotating source. The gravitational gyrofactor for spin is identified. The charged case (Kerr-Newman) is studied using a minimal prescription for electromagnetic coupling in the locally inertial frame, and to the leading order the standard electromagnetic gyrofactor is retrieved. A first-order perturbation calculation of the shift of the Schwarzschild energy level yields the main interesting result of this work: anomalous Zeeman splitting of the energy level of a Dirac particle in the Kerr metric.