Abstract
The weak field-low velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a ‘dipole-dipole’ interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally inertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzschild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.
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Iyer, B.R., Kumar, A. Dirac equation in Kerr space-time. Pramana - J. Phys. 8, 500–511 (1977). https://doi.org/10.1007/BF02872098
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DOI: https://doi.org/10.1007/BF02872098