Deflection of light by rotating regular black holes using the Gauss-Bonnet theorem

TL;DR

This paper investigates the weak gravitational lensing effects of rotating regular black holes, calculating light deflection angles using the Gauss-Bonnet theorem and geodesic methods, revealing parameter-dependent corrections beyond Kerr black holes.

Contribution

It introduces a novel application of the Gauss-Bonnet theorem to compute light deflection in rotating regular black holes with additional parameters, extending beyond Kerr solutions.

Findings

Deflection angles depend on electric and magnetic charges, and deviation parameters.

The Gauss-Bonnet theorem provides a topological perspective on gravitational lensing.

Results are verified via geodesic formalism, showing consistency and new correction terms.

Abstract

In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-Garc\'ia (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the Gauss-Bonnet theorem (GBT) and show that the deflection of light can be viewed as a partially topological effect in which the deflection angle can be calculated by considering a domain outside of the light ray applied to the black hole optical geometries. Then, we demonstrate also the deflection angle via the geodesics formalism for these black holes to verify our results and explore the differences with the Kerr solution. These black holes have in addition to the total mass and rotation parameter, different parameters as electric charge, magnetic charge, and deviation parameter. Newsworthy, we find that the deflection of light has correction terms coming from these parameters which generalizes the Kerr deflection angle.