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Register a new userKerr-Newman-Jacobi geometry and the deflection of charged massive particles
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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 particles charge.
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We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted by the particles initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.
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.
We use Heun type solutions given in cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.
We investigate the conjecture on the upper bound of the Lyapunov exponent for the chaotic motion of a charged particle around a Kerr-Newman black hole. The Lyapunov exponent is closely associated with the maximum of the effective potential with respect to the particle. We show that when the angular momenta of the black hole and particle are considered, the Lyapunov exponent can exceed the conjectured upper bound. This is because the angular momenta change the effective potential and increase the magnitude of the chaotic behavior of the particle. Furthermore, the location of the maximum is also related to the value of the Lyapunov exponent and the extremal and non-extremal states of the black hole.
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