The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach

In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the Jacobi-Maupertuis Randers-Finsler metric. More specifically,we apply the Gauss-Bonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical metric and geodesic curvature of particles orbit. In particular, the finite-distance correction to the deflection angle of signal with general velocity in the the Kerr black hole and Teo wormhole spacetimes are considered. Our results cover the previous work of the deflection angle of light, as well as the deflection angle of massive particles in the limit for the receive and source at infinite distance from the lens object. In Kerr black hole spacetime, we compared the effects due to the black hole spin, the finite-distance of source or receiver, and the relativistic velocity in microlensings and lensing by galaxies. It is found in these cases, the effect of BH spin is usually a few orders larger than that of the finite-distance and relativistic velocity, while the relative size of the latter two could vary according to the particle velocity, source or observer distance and other lensing parameters.Comment: 16 pages, 4 figure

Deflection of charged signals in a dipole magnetic field in Schwarzschild background using Gauss-Bonnet theorem

This paper studies the deflection of charged particles in a dipole magnetic field in Schwarzschild spacetime background in the weak field approximation. To calculate the deflection angle, we use Jacobi metric and Gauss-Bonnet theorem. Since the corresponding Jacobi metric is a Finsler metric of Randers type, we use both the osculating Riemannian metric method and generalized Jacobi metric method. The deflection angle up to fourth order is obtained and the effect of the magnetic field is discussed. It is found that the magnetic dipole will increase (or decrease) the deflection angle of a positively charged signal when its rotation angular momentum is parallel (or antiparallel) to the magnetic field. It is argued that the difference in the deflection angles of different rotation directions can be viewed as a Finslerian effect of the non-reversibility of the Finsler metric. The similarity of the deflection angle in this case with that for the Kerr spacetime allows us to directly use the gravitational lensing results in the latter case. The dependence of the apparent angles on the magnetic field suggests that by measuring these angles the magnetic dipole might be constrained.Comment: 13 pages, 3 figure

The deflection of charged massive particles by a 4-Dimensional charged Einstein-Gauss-Bonnet black hole

Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel 4-dimensional charged Einstein-Gauss-Bonnet black hole. We focus on the weak-filed approximation and consider the deflection angle with finite-distance effects, i.e. the source and observer at finite distances from the black hole. To this end, we use a geometric and topological method, which is to apply the Gauss-Bonnet theorem to the Jacobi-metric surface to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution $\delta_g$, a pure electrostatic one $\delta_c$ 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.Comment: 11 pages, 5 Figures; conclusion part improved and reference adde

Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes

Using a perturbative technique, in this work we study the deflection of null and timelike signals in the extended Einstein-Maxwell spacetime, the Born-Infeld gravity and the charged Ellis-Bronnikov (CEB) spacetime in the weak field limit. The deflection angles are found to take a (quasi-)series form of the impact parameter, and automatically takes into account the finite distance effect of the source and observer. The method is also applied to find the deflections in CEB spacetime with arbitrary dimension. It's shown that to the leading non-trivial order, the deflection in some $n$-dimensional spacetimes is of the order $\mathcal{O}(M/b)^{n-3}$. We then extended the method to spacetimes that are asymptotically non-flat and studied the deflection in a nonlinear electrodynamical scalar theory. The deflection angle in such asymptotically non-flat spacetimes at the trivial order is found to be not $\pi$ anymore. In all these cases, the perturbative deflection angles are shown to agree with numerical results extremely well. The effects of some nontrivial spacetime parameters as well as the signal velocity on the deflection angles are analyzed.Comment: 30 pages, 7 figures; title modified; to match published version in Class.Quant.Gra

Effect of ecological restoration programs on dust concentrations in the North China Plain: a case study

In recent decades, the Chinese government has made a great effort in initiating large-scale ecological restoration programs (ERPs) to reduce the dust concentrations in China, especially for dust storm episodes. Using the Moderate Resolution Imaging Spectroradiometer (MODIS) land cover product, the ERP-induced land cover changes are quantitatively evaluated in this study. Two obvious vegetation protective barriers arise throughout China from the southwest to the northeast, which are well known as the "Green Great Wall" (GGW). Both the grass GGW and forest GGW are located between the dust source region (DSR) and the densely populated North China Plain (NCP). To assess the effect of ERPs on dust concentrations, a regional transport/dust model (WRF-DUST, Weather Research and Forecast model with dust) is applied to investigate the evolution of dust plumes during a strong dust storm episode from 2 to 8 March 2016. The WRF-DUST model generally performs reasonably well in reproducing the temporal variations and spatial distributions of near-surface [PMC] (mass concentration of particulate matter with aerodynamic diameter between 2.5 and 10 mu m) during the dust storm event. Sensitivity experiments have indicated that the ERP-induced GGWs help to reduce the dust concentration in the NCP, especially in BTH (Beijing, Tianjin, and Hebei). When the dust storm is transported from the upwind DSR to the downwind NCP, the [PMC] reduction ranges from -5 to -15% in the NCP, with a maximum reduction of -12.4% (-19.2 mu gm(3)) in BTH and -7.6% (-10.1 mu g m(3)) in the NCP. We find the dust plumes move up to the upper atmosphere and are transported from the upwind DSR to the downwind NCP, accompanied by dust decrease. During the episode, the forest GGW is nonsignificant in dust concentration control because it is of benefit for dry deposition and not for emission. Conversely, the grass GGW is beneficial in controlling dust erosion and is the dominant reason for [PMC] decrease in the NCP. Because the air pollution is severe in eastern China, especially in the NCP, and the contribution of dust episodes is significant, the reduction of dust concentrations will have important effects on severe air pollution. This study illustrates the considerable contribution of ERPs to the control of air pollution in China, especially in springtime