Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

TL;DR

This paper calculates the deflection angle of charged particles in Kerr-Newman spacetime using three geometric methods, revealing how black hole spin and charge influence particle trajectories.

Contribution

It introduces a novel calculation of the second-order deflection angle for charged particles in Kerr-Newman spacetime using multiple geometric approaches.

Findings

Black hole spin affects deflection gravitationally and magnetically.

Deflection angle depends on charge-to-energy ratio and black hole parameters.

Three methods yield consistent second-order deflection angles.

Abstract

In this paper, we investigate the deflection of a charged particle moving in the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To this end, we use the Jacobi geometry, which can be described in three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and $(n+1)$-dimensional stationtary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and the generalized Jacobi metric method to study the deflection angle, respectively. In the $(n+1)$-dimensional spacetime picture, the motion of charged particle follows the null geodesic, and thus we use the standard geodesic method to calculate the deflection angle. Three methods lead to the same second-order deflection angle, which is obtained for the first time. The result shows that the black hole spin $a$ affects the deflection of charged particles both gravitationally and magnetically at the leading order (order $\mathcal{O}([M]^2/b^2)$). When $qQ/E<2M$, $a$ will decrease (or increase) the deflection of prograde (or retrograde) charged signal. If $qQ/E> 2M$, the opposite happens, and the ray is divergently deflected by the lens. We also showed that the effect of the magnetic charge of the dyonic Kerr-Newman black hole on the deflection angle is independent of the particle's charge.