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

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 the Randers-Finsler metric, the Zermelo navigation problem, and the ($n+1$)-dimensional stationary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize the osculating Riemannian manifold method and the generalized Jacobi metric method, respectively, to study the deflection angle. 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. The 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 [$\mathcal{O}([M{]}^{2}/{b}^{2})$]. 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 show 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.

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