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

TL;DR

This paper investigates how charged massive particles are deflected by a novel four-dimensional charged Einstein-Gauss-Bonnet black hole using geometric methods, revealing the influences of charges, velocities, and coupling constants on the deflection angle.

Contribution

It introduces a geometric-topological approach using the Gauss-Bonnet theorem to calculate particle deflection angles in this specific black hole spacetime, including finite distance effects.

Findings

Deflection angle comprises gravitational, electrostatic, and coupling contributions.

Electrostatic contribution can be computed in flat spacetime using the Jacobi metric.

Deflection angle varies with the Gauss-Bonnet coupling constant and particle parameters.

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.