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

Abstract

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