Non-equatorial deflection of light due to Kerr–Newman black hole: a material medium approach

Abstract We explored the effect of space-time geometry on the trajectory of light rays in the context of a charged, rotating black hole. We derived an analytical expression for the deflection of light rays in Kerr–Newman space-time geometry, using a material medium approach, on non-equatorial plane. From this deflection angle expression it is evident that the charge and rotation of the black hole can affect the light rays’ paths. For Kerr–Newman geometry, the deflection angle decreases with increasing charge when the rotation parameter is held constant. Conversely, for a constant charge, the deflection angle increases with the rotation parameter for prograde and decreases for retrograde trajectories. Applying both factors results in the deflection angle being lower than that of the Schwarzschild geometry. Non-equatorial study of the deflection angle reveals that it is maximum in the equatorial plane than in the pole. The frame-dragging effects in the Kerr–Newman field were taken into account to calculate the velocity of light rays, leading to the determination of the refractive index in this field geometry. This study concludes that, depending on the values of the rotation parameter and charge parameter, both prograde and retrograde trajectories coincide, result in that at some point the frame dragging effect is the same for prograde and retrograde motion. Also, the frame dragging effect increases towards poles than the equatorial plane, and this nontrivial nature results because of the interplay between charge, rotation parameter and rotation frequency of the black hole.