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

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.

14 pages, 1 figure, to appear in PRD

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• Superentropic Black Hole Shadows in Arbitrary Dimensions
• Extending Gibbons-Werner method to bound orbits of massive particles
• Deflection of charged signals in a dipole magnetic field in Schwarzschild background using Gauss-Bonnet theorem
• Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos
• Effect of electric interaction on the deflection and gravitational lensing in the strong field limit
• Weak gravitational lensing by an ESTGB black hole in the presence of a plasma
• Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes
• Modelling the Sgr A${}^{\ast }$ and M87${}^{\ast }$ shadows by using the Kerr-Taub-NUT metrics in the presence of a scalar field
• Boundary-only weak deflection angles from isothermal optical geometry
• Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes
• Massive particle surfaces and black hole shadows from intrinsic curvature
• The influence of cosmological constant on light deflection in rotating spacetimes via the generalized Gibbons-Werner method