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.

The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green’s functions are written down in the two causally disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green’s functions in all regions is exhibited.

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.

We analyze the accretion of charged matter onto a rotating black hole immersed in an aligned dipolar magnetic field. We specialize to motion in the equatorial plane and calculate the ‘Keplerian’ angular momentum distribution, the marginally stable and marginally bound orbits, and the efficiency of mass-to-energy conversion as functions of the angular momentum of the black hole and of the product of the dipole moment and the charge of the infalling matter. Although the detailed results are quite different from those previously obtained in the case of an uniform magnetic field, the astrophysically relevant results are very similar; when hydrodynamical accretion is considered, these effects of the magnetic field are always very small. But for test particles the efficiency can be significantly increased for limited ranges of the parameters.

The Vaidya metric representing the gravitational field of a radiating star is generalized to spacetimes of dimensions greater than four.