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.

11 pages, figures updated and language polished;

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Cited by in corpus (2)

• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Deriving Weak Deflection Angle by Black Holes or Wormholes using Gauss-Bonnet Theorem