Mathematical analysis of gravitational deflection angle of light for Bardeen type black holes

The gravitational deflection angle of light is crucial in various areas like astrophysics, cosmology and astronomy since it serves as a major tool for testing general relativity and its modification of gravitational theory. This paper studied the problem of the gravitational deflection angle of light for Bardeen type black holes and rotating Bardeen type black holes generated by Einstein gravitational field equations coupled with nonlinear electrodynamics. Through the theoretical analysis of the gravitational deflection angle of light for Bardeen type black holes and rotating Bardeen type black holes with geodesic analysis method, we come up with the corresponding expressions of it. Subsequently, we use mathematical tools to calculate its value. The results show that the gravitational deflection angle of light for Bardeen type black holes is smaller than that of classical Einstein in all circumstances, while the rotating Bardeen type black holes hold a smaller gravitational deflection angle of light than that of the rotating Kerr black holes. In particular, the existence of magnetic charge g and the rotation parameter a in nonlinear electrodynamics could reduce the gravitational deflection angle of light.