Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole

Abstract

Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein-Gauss-Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss-Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution $\delta_g$, a pure electrostatic $\delta_c$ and a gravitational-electrostatic coupling term $\delta_{gc}$. We also show that the electrostatic contribution $\delta_c$ can also be computed by the Jacobi metric method using the GB theorem to a charge in a Minkowski flat spacetime background. We find that the deflection angle increases(decreases) if the Gauss-Bonnet coupling constant $\alpha$ is negative(positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.