scholarly journals Deflection angle of light for an observer and source at finite distance from a rotating wormhole

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
Toshiaki Ono ◽  
Asahi Ishihara ◽  
Hideki Asada
Keyword(s):  
Deflection Angle ◽  
Finite Distance

scholarly journals Finite-Distance Gravitational Deflection of Massive Particles by the Kerr-like Black Hole in the Bumblebee Gravity Model

2019 ◽  
Author(s):  
Zonghai Li ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravity Model ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Geodesic Curvature ◽  
Surface Integral ◽  
Massive Particles ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Gravitational Deflection

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

scholarly journals General relativistic aberration equation and measurable angle of light ray in Kerr spacetime

2021 ◽  
pp. 2150045
Author(s):  
Hideyoshi Arakida
Keyword(s):  
Deflection Angle ◽  
Transverse Velocity ◽  
Null Geodesic ◽  
Transverse Motion ◽  
Static Case ◽  
Kerr Spacetime ◽  
Frame Dragging ◽  
Finite Distance ◽  
General Relativistic ◽  
The Impact

We will mainly discuss the measurable angle (local angle) of the light ray [Formula: see text] at the position of the observer [Formula: see text] instead of the total deflection angle (global angle) [Formula: see text] in Kerr spacetime. We will investigate not only the effect of the gravito-magnetic field or frame dragging due to the spin of the central object but also the contribution of the motion of the observer with a coordinate radial velocity [Formula: see text] and a coordinate transverse velocity [Formula: see text] where [Formula: see text] is the impact parameter ([Formula: see text] and [Formula: see text] are the angular momentum and the energy of the light ray, respectively) and [Formula: see text] is a coordinate angular velocity. [Formula: see text] and [Formula: see text] are computed from the components of the four-velocity of the observer [Formula: see text] and [Formula: see text], respectively. Because the motion of observer causes an aberration, we will employ the general relativistic aberration equation to obtain the measurable angle [Formula: see text] which is determined by the four-momentum of the light ray [Formula: see text] and the four-momentum of the radial null geodesic [Formula: see text] as well as the four-velocity of the observer [Formula: see text]. The measurable angle [Formula: see text] given in this paper can be applied not only to the case of the observer located in an asymptotically flat region but also to the case of the observer placed within the curved and finite-distance region. Moreover, when the observer is in radial motion, the total deflection angle [Formula: see text] can be expressed by [Formula: see text]; this is consistent with the overall scaling factor [Formula: see text] instead of [Formula: see text] with respect to the total deflection angle [Formula: see text] in the static case ([Formula: see text] is the velocity of the lens object). On the other hand, when the observer is in transverse motion, the total deflection angle is given by the form [Formula: see text] if we define the transverse velocity as having the form [Formula: see text].

scholarly journals Deriving Weak Deflection Angle by Black Holes or Wormholes using Gauss-Bonnet Theorem

2021 ◽  
Author(s):  
Yashmitha Kumaran ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Plasma Medium ◽  
Asymptotically Flat ◽  
Finite Distance ◽  
Flat Spacetimes ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

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

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Zonghai Li ◽  
Junji Jia
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Kerr Black Hole ◽  
Relativistic Velocity ◽  
Massive Particles ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Jacobi Metric ◽  
Optical Metric ◽  
Gravitational Deflection

Abstract 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 receiver 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 black hole 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.

scholarly journals Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole

2021 ◽  
Author(s):  
Zonghai Li ◽  
Yujie Duan ◽  
Junji Jia
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Massive Particle ◽  
Field Approximation ◽  
Weak Field ◽  
Coupling Constant ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Electrostatic Coupling ◽  
Bonnet Theorem

Abstract 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 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.

scholarly journals The Effects of Finite Distance on the Gravitational Deflection Angle of Light

Universe ◽  
2019 ◽  
Vol 5 (11) ◽  
pp. 218 ◽  
Author(s):  
Toshiaki Ono ◽  
Hideki Asada
Keyword(s):  
Deflection Angle ◽  
Short Review ◽  
Light Deflection ◽  
Sagittarius A ◽  
Distance Effects ◽  
Gravitational Deflection Of Light ◽  
Finite Distance ◽  
Definition Of ◽  
Distance Limit ◽  
Gravitational Deflection

In order to clarify the effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss–Bonnet (GB) theorem in differential geometry (Ishihara et al. 2016). The purpose of the present paper is to give a short review of a series of works initiated by the above paper. First, we provide the definition of the gravitational deflection angle of light for the finite-distance source and receiver in a static, spherically symmetric and asymptotically flat spacetime. We discuss the geometrical invariance of the definition by using the GB theorem. The present definition is used to discuss finite-distance effects on the light deflection in Schwarzschild spacetime for both the cases of weak deflection and strong deflection. Next, we extend the definition to stationary and axisymmetric spacetimes. We compute finite-distance effects on the deflection angle of light for Kerr black holes and rotating Teo wormholes. Our results are consistent with the previous works if we take the infinite-distance limit. We briefly mention also the finite-distance effects on the light deflection by Sagittarius A * .

scholarly journals Static Aeroelastic Characteristics of Morphing Trailing-Edge Wing Using Geometrically Exact Vortex Lattice Method

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Sen Mao ◽  
Changchuan Xie ◽  
Lan Yang ◽  
Chao Yang
Keyword(s):  
Vortex Lattice ◽  
Deflection Angle ◽  
Aircraft Design ◽  
Analysis Method ◽  
Lattice Method ◽  
Trailing Edge ◽  
Vortex Lattice Method ◽  
Analysis And Design ◽  
Aeroelastic Analysis ◽  
Typical Model

A morphing trailing-edge (TE) wing is an important morphing mode in aircraft design. In order to explore the static aeroelastic characteristics of a morphing TE wing, an efficient and feasible method for static aeroelastic analysis has been developed in this paper. A geometrically exact vortex lattice method (VLM) is applied to calculate the aerodynamic forces. Firstly, a typical model of a morphing TE wing is chosen and built which has an active morphing trailing edge driven by a piezoelectric patch. Then, the paper carries out the static aeroelastic analysis of the morphing TE wing and corresponding simulations were carried out. Finally, the analysis results are compared with those of a traditional wing with a rigid trailing edge using the traditional linearized VLM. The results indicate that the geometrically exact VLM can better describe the aerodynamic nonlinearity of a morphing TE wing in consideration of geometrical deformation in aeroelastic analysis. Moreover, out of consideration of the angle of attack, the deflection angle of the trailing edge, among others, the wing system does not show divergence but bifurcation. Consequently, the aeroelastic analysis method proposed in this paper is more applicable to the analysis and design of a morphing TE wing.

scholarly journals Frequency Division Multiplexing of Terahertz Waves Realized by Diffractive Optical Elements

2021 ◽  
Vol 11 (14) ◽  
pp. 6246
Author(s):  
Paweł Komorowski ◽  
Patrycja Czerwińska ◽  
Mateusz Kaluza ◽  
Mateusz Surma ◽  
Przemysław Zagrajek ◽  
...  
Keyword(s):  
Frequency Division Multiplexing ◽  
Diffractive Optical Elements ◽  
Frequency Division ◽  
Terahertz Waves ◽  
Optical Elements ◽  
Telecommunication Systems ◽  
Wide Range ◽  
The Future ◽  
Wireless Telecommunication ◽  
Finite Distance

Recently, one of the most commonly discussed applications of terahertz radiation is wireless telecommunication. It is believed that the future 6G systems will utilize this frequency range. Although the exact technology of future telecommunication systems is not yet known, it is certain that methods for increasing their bandwidth should be investigated in advance. In this paper, we present the diffractive optical elements for the frequency division multiplexing of terahertz waves. The structures have been designed as a combination of a binary phase grating and a converging diffractive lens. The grating allows for differentiating the frequencies, while the lens assures separation and focusing at the finite distance. Designed structures have been manufactured from polyamide PA12 using the SLS 3D printer and verified experimentally. Simulations and experimental results are shown for different focal lengths. Moreover, parallel data transmission is shown for two channels of different carrier frequencies propagating in the same optical path. The designed structure allowed for detecting both signals independently without observable crosstalk. The proposed diffractive elements can work in a wide range of terahertz and sub-terahertz frequencies, depending on the design assumptions. Therefore, they can be considered as an appealing solution, regardless of the band finally used by the future telecommunication systems.

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