scholarly journals Gravitational Lensing of Charged Ayon-Beato-Garcia Black Holes and Nonlinear Effects of Maxwell Fields

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
H. Ghaffarnejad ◽  
M. Amirmojahedi ◽  
H. Niad
Keyword(s):  
Central Region ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Nonlinear Effects ◽  
Angular Separation ◽  
De Sitter ◽  
Static Black Hole ◽  
Light Rays ◽  
Maxwell Fields ◽  
Bending Light

Nonsingular Ayon-Beato-Garcia (ABG) spherically symmetric static black hole (BH) with charge to mass ratio q=g/2m is metric solution of Born Infeld nonlinear Maxwell-Einstein theory. Central region of the BH behaves as (anti-)de Sitter for (|q|>1)  |q|<1. In the case where |q|=1, the BH central region behaves as Minkowski flat metric. Nonlinear Electromagnetic (NEM) fields counterpart causes deviation of light geodesics and so light rays will be forced to move on from effective metric. In this paper we study weak and strong gravitational lensing of light rays by seeking effects of NEM fields counterpart on image locations and corresponding magnification. We set our calculations to experimentally observed Sgr A⁎ BH. In short we obtained the following: for large distances, the NEM counterpart is negligible and it reduces to linear Maxwell fields. The NEM field enlarges radius of the BH photon sphere linearly by raising |q|>1 but decreases by raising |q|≤1. Sign of deflection angle of bending light rays is changed in presence of NEM effects with respect to ones obtained in absence of NEM fields. Absolute value of deflection angle rises by increasing |q|→1. Image locations in weak deflection limit (WDL) decrease (increases) by raising 0<|q|<1 in presence (absence) of NEM fields. By raising the closest distance of the bending light rays image locations in WDL change from left (right) to right (left) in absence (presence) of NEM fields. In WDL, radius of Einstein rings and corresponding magnification centroid become larger (smaller) in presence (absence) of NEM fields. Angular separation called s between the innermost and outermost relativistic images increases (decreases) by increasing 0<|q|<1 in absence (presence) of NEM fields. Corresponding magnification r decreases (increases) by raising 0<|q|<1 in absence (presence) of NEM fields.

scholarly journals A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing

1996 ◽  
Vol 173 ◽  
pp. 281-282
Author(s):  
A. O. Petters
Keyword(s):  
Light Source ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Gravitational Lens ◽  
Source Plane ◽  
Lens System ◽  
Light Rays ◽  
Counting Formula

Consider a gravitational lens system with K planes. If light rays are traced back from the observer to the light source plane, then the points on the first lens plane where a light ray either terminates, or, passes through and terminates before reaching the light source plane, are “obstruction points.” More precisely, tracing rays back to the source plane induces a K-plane lensing map η : U ⊆ R2 → R2 of the form η(x1) = x1 −∑i=1k αi(xi(xi)). We then define an obstruction point of η to be a point a of U where limx1→a |αi(xi(x1))| = ∞ for some “deflection angle” αi.

GRAVITATIONAL LENSING IN AN ENERGY-DEPENDENT SPACETIME METRIC

2012 ◽  
Vol 21 (01) ◽  
pp. 1250007 ◽  
Author(s):  
A. F. GRILLO ◽  
E. LUZIO ◽  
F. MÉNDEZ ◽  
F. TORRES
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Lorentz Invariance ◽  
Angular Separation ◽  
Weak Limit ◽  
Corrective Term ◽  
Gravitational Source ◽  
Different Types ◽  
Energy Dependent ◽  
Planck Energy

In this article, we explore the consequences in the calculation of deflection angle of photons, caused by a gravitational source of mass M, for the case of an energy dependent metric. We analyze the corrections to the standard Schwarzschild case for the weak and strong limits. In both cases, the corrections to the deflection angle are of the order ϵ/E Pl , where E Pl is the Planck energy and ϵ, the energy of the photon at spatial infinite. The corrections to the angular separation image is also of order ϵ/E Pl , for the weak limit, while in the strong case there is a corrective term with the shape ϵ/E Pl n e2nπ for the relativistic image of order n. The amplification of the image is also discussed. Even if corrections are tiny, in both limits, we discuss the qualitative effects for different types of Lorentz invariance deformations.

scholarly journals Gravitational lensing by charged black hole in regularized 4D Einstein–Gauss–Bonnet gravity

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Rahul Kumar ◽  
Shafqat Ul Islam ◽  
Sushant G. Ghosh
Keyword(s):  
Black Holes ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
Angular Position ◽  
Angular Separation ◽  
Light Deflection ◽  
Charged Black Holes ◽  
The Deflection Angle ◽  
Sgr A

AbstractAmong the higher curvature gravities, the most extensively studied theory is the so-called Einstein–Gauss–Bonnet (EGB) gravity, whose Lagrangian contains Einstein term with the GB combination of quadratic curvature terms, and the GB term yields nontrivial gravitational dynamics in $$ D\ge 5$$ D ≥ 5 . Recently there has been a surge of interest in regularizing, a $$ D \rightarrow 4 $$ D → 4 limit of, the EGB gravity, and the resulting regularized 4D EGB gravity valid in 4D. We consider gravitational lensing by Charged black holes in the 4D EGB gravity theory to calculate the light deflection coefficients in strong-field limits $$\bar{a}$$ a ¯ and $$\bar{b}$$ b ¯ , while former increases with increasing GB parameter $$\alpha $$ α and charge q, later decrease. We also find a decrease in the deflection angle $$\alpha _D$$ α D , angular position $$\theta _{\infty }$$ θ ∞ decreases more slowly and impact parameter for photon orbits $$u_{m}$$ u m more quickly, but angular separation s increases more rapidly with $$\alpha $$ α and charge q. We compare our results with those for analogous black holes in General Relativity (GR) and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes Sgr A* and M87*.

scholarly journals Weak Deflection Angle of Kazakov-Solodukhin Black Hole in Plasma Medium

2021 ◽  
Author(s):  
Wajiha Javed ◽  
Iqra Hussain ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deformation Parameter ◽  
Deflection Angle ◽  
Modern Method ◽  
Observational Evidence ◽  
Plasma Medium ◽  
Light Rays ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle.

scholarly journals Effect of Aether Field on Weak Deflection Angle of Black Holes

2019 ◽  
Author(s):  
Ali Övgün ◽  
İzzet Sakallı ◽  
Joel Saavedra
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Limit ◽  
Spherically Symmetric ◽  
Light Rays ◽  
Topological Effect ◽  
The Deflection Angle ◽  
Bonnet Theorem ◽  
Limit Approximation

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

scholarly journals Numerical methods for General Relativistic particles

2018 ◽  
Vol 14 (S342) ◽  
pp. 19-23
Author(s):  
Fabio Bacchini ◽  
Bart Ripperda ◽  
Alexander Y. Chen ◽  
Lorenzo Sironi
Keyword(s):  
Numerical Methods ◽  
Gravitational Lensing ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Numerical Algorithms ◽  
Relativistic Effects ◽  
Compact Objects ◽  
Light Rays ◽  
Massive Particles ◽  
External Forces

AbstractWe present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Efficient numerical methods are required for solving the equations of motion and compute i) the black hole shadow obtained by tracing light rays from the object to a distant observer, and ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present generalized algorithms capable of simulating ensembles of photons or massive particles in any spacetime, with the option of including external forces. The coupling of these tools with GRMHD simulations is the key point for obtaining insight on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.

scholarly journals Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sharif ◽  
Sehrish Iftikhar
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Galactic Center ◽  
Deflection Angle ◽  
Orbital Motion ◽  
Strong Field ◽  
Schwarzschild Black Hole ◽  
Field Limit ◽  
Null Geodesics ◽  
Supermassive Black Hole

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole.

scholarly journals Traversable wormholes in Einsteinian cubic gravity

2019 ◽  
Vol 35 (06) ◽  
pp. 2050017 ◽  
Author(s):  
Mohammad Reza Mehdizadeh ◽  
Amir Hadi Ziaie
Keyword(s):  
Equation Of State ◽  
Gravitational Lensing ◽  
Energy Condition ◽  
Higher Order ◽  
Energy Conditions ◽  
Geodesic Motion ◽  
De Sitter ◽  
Asymptotically Flat ◽  
Traversable Wormholes ◽  
Standard Energy

In this work, we investigate wormhole configurations described by a constant redshift function in Einstein-Cubic gravity ( ECG ). We derive analytical wormhole geometries by assuming a particular equation of state ( EoS ) and investigate the possibility that these solutions satisfy the standard energy conditions. We introduce exact asymptotically flat and anti-de Sitter (AdS) spacetimes that admit traversable wormholes. These solutions are obtained by imposing suitable values for the parameters of the theory so that the resulted geometries satisfy the weak energy condition ( WEC ) in the vicinity of the throat, due to the presence of higher-order curvature terms. Moreover, we find that AdS solutions satisfy the WEC throughout the spacetime. A description of the geodesic motion of time-like and null particles is presented for the obtained wormhole solutions. Also, using gravitational lensing effects, observational features of the wormhole structure are discussed.

Demonstrating Gravitational Lensing Using Solar Eclipses

2021 ◽  
Vol 03 (03) ◽  
pp. 2150009
Author(s):  
Gillian Foo ◽  
Jhoon Yong Tan ◽  
Edmund Yuen ◽  
Laurentcia Arlany ◽  
A. Yang ◽  
...  
Keyword(s):  
Gravitational Lensing ◽  
Angular Separation ◽  
Total Solar Eclipse ◽  
Light Deflection ◽  
Interesting Paper ◽  
National University ◽  
Solar Eclipses ◽  
The Individual ◽  
Pixel Scale ◽  
Plate Solution

As encouraged by the interesting paper “Solar eclipses as a teaching opportunity in relativity” by Overduin et al.,awe made measurements of the angular deflections of neighboring stars during the 9 March 2016 total solar eclipse as imaged by National University of Singapore (NUS) students, to verify a result of general relativity. In this project, we used these images and measured the stars’ pixel positions and transformed them to equatorial coordinates using a similar approach to Overduin et al., with a few modifications. Instead of solving to determine the pixel scale and rotation, we performed a plate solution using the software AstroImageJ which enables accounting for the image’s higher order distortion. This data is found in the image’s Flexible Image Transport System (FITS) header. Image star pair separations were then compared to their database separations after determining how the individual deflections affect angular separation. Our experimental results have large uncertainties and were deemed imprecise to confirm the effects of gravitational light deflection. We include a detailed analysis and discussion on this educational project.

Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

2016 ◽  
Vol 25 (09) ◽  
pp. 1641011 ◽  
Author(s):  
Mengjie Wang
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Boundary Conditions ◽  
Energy Flux ◽  
Momentum Flux ◽  
De Sitter ◽  
Perturbative Methods ◽  
Flux Boundary Conditions ◽  
Maxwell Fields ◽  
New Type

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

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