Equatorial light bending around Kerr-Newman black holes

TL;DR

This paper derives a closed-form expression for the deflection angle of light around charged, spinning black holes, revealing how charge influences light trajectories and the apparent shape of such black holes.

Contribution

It provides a detailed analysis and a closed-form formula for light deflection in Kerr-Newman black holes, highlighting the effects of charge on light trajectories.

Findings

Charge increases lead to stronger repulsive effects on light rays.

The radius of the innermost circular light orbit decreases with increasing charge.

Deflection angle decreases as black hole charge increases for fixed impact parameter.

Abstract

We study the deflection angle of a light ray as it traverses on the equatorial plane of a charged spinning black hole. We provide detailed analysis of the light ray's trajectory, and derive the closed-form expression of the deflection angle due to the black hole in terms of elliptic integrals. In particular, the geodesic equation of the light ray along the radial direction can be used to define an appropriate ``effective potential". The nonzero charge of the black hole shows stronger repulsive effects to prevent light rays from falling into the black hole as compared with the Kerr case. As a result, the radius of the innermost circular motion of light rays with the critical impact parameter decreases as charge $Q$ of the black hole increases for both direct and retrograde motions. Additionally, the deflection angle decreases when $Q$ increases with the fixed impact parameter. These results will have a direct consequence on constructing the apparent shape of a rotating charged black hole.