Weak deflection angle by electrically and magnetically charged black holes from nonlinear electrodynamics

Abstract

Nonlinear electrodynamic (NLED) theories are well motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in the search for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED---the Euler-Heisenberg NLED model and the Bronnikov NLED model---and calculate the weak deflection angle of light and charged particles by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynamics on the deflection angle and analyze the behavior of the deflection angle by a regular magnetically charged black hole. It is found that both the electric and magnetic charges of the black hole reduce the weak deflection angle, and the one-loop corrections make a positive contribution to the deflection angle, but their influence is deeply suppressed by the impact parameter. For the charged particles, due to electrostatic interaction, the weak deflection angle changes noticeably and the influence of the one-loop corrections is enhanced. We find that the regular magnetically charged black hole based on the Bronnikov NLED model has a smaller deflection angle than the singular one. We also calculate the deflection angle of light by the geodesic method for verification. In addition, we discuss the effects of a cold nonmagnetized plasma on the deflection angle and find that the deflection angle increases with the plasma parameter.