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 Effect of Non-Linear Electrodynamics on Weak Field Deflection Angle by Black Hole

2020 ◽  
Author(s):  
Wajiha Javed ◽  
Ali Hamza ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Weak Limit ◽  
Spacetime Geometry ◽  
Weak Gravitational Field ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field.

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 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 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.

Nonlocal Gravity

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
Gravitational Field ◽  
Gravitational Lensing ◽  
Past History ◽  
Lorentz Invariance ◽  
Minkowski Spacetime ◽  
Field Measurements ◽  
Local Principle ◽  
History Of ◽  
Expansion Of The Universe ◽  
Nearby Galaxies

A postulate of locality permeates through the special and general theories of relativity. First, Lorentz invariance is extended in a pointwise manner to actual, namely, accelerated observers in Minkowski spacetime. This hypothesis of locality is then employed crucially in Einstein’s local principle of equivalence to render observers pointwise inertial in a gravitational field. Field measurements are intrinsically nonlocal, however. To go beyond the locality postulate in Minkowski spacetime, the past history of the accelerated observer must be taken into account in accordance with the Bohr-Rosenfeld principle. The observer in general carries the memory of its past acceleration. The deep connection between inertia and gravitation suggests that gravity could be nonlocal as well and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein’s theory of gravitation has recently been developed. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. A significant observational consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. The implications of NLG are explored in this book for gravitational lensing, gravitational radiation, the gravitational physics of the Solar System and the internal dynamics of nearby galaxies as well as clusters of galaxies. This approach is extended to nonlocal Newtonian cosmology, where the attraction of gravity fades with the expansion of the universe. Thus far only some of the consequences of NLG have been compared with observation.

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.

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.

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

scholarly journals Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Junji Jia ◽  
Ke Huang
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
Distance Effect ◽  
Critical Value ◽  
Field Limit ◽  
Perturbative Method ◽  
The Deflection Angle ◽  
The Impact ◽  
Strong Field Limit

AbstractA perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $$(1-b_c/b)$$ ( 1 - b c / b ) where b is the impact parameter and $$b_c$$ b c is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter l and the asymptotic velocity v of the signal. The BH shadow size were found to decrease slightly as l increases to its critical value, and increase as v decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of l and decrease of v will increase their values.

scholarly journals Modeling spectral lags in active galactic nucleus flares in the context of Lorentz invariance violation searches

2020 ◽  
Vol 633 ◽  
pp. A143 ◽  
Author(s):  
C. Perennes ◽  
H. Sol ◽  
J. Bolmont
Keyword(s):  
Lorentz Invariance ◽  
High Energy ◽  
Physical Parameters ◽  
New Era ◽  
Invariance Violation ◽  
Quantum Gravity Phenomenology ◽  
Lorentz Invariance Violation ◽  
Very High Energy ◽  
Energy Dependent ◽  
New Generation

Context. High-energy photons emitted by flaring active galactic nuclei (AGNs) have been used for many years to constrain modified dispersion relations in vacuum encountered in the context of quantum gravity phenomenology. In such studies, done in the GeV–TeV range, energy-dependent delays (spectral lags) are searched for, usually neglecting any source-intrinsic time delay. Aims. With the aim being to distinguish Lorentz invariance violation (LIV) effects from lags generated at the sources themselves, a detailed investigation into intrinsic spectral lags in flaring AGNs above 100 GeV is presented in the frame of synchrotron-self-Compton scenarios for their very-high-energy (VHE) emission. Methods. A simple model of VHE flares in blazars is proposed, allowing to explore the influence of the main physical parameters describing the emitting zones on intrinsic delays. Results. For typical conditions expected in TeV blazars, significant intrinsic lags are obtained, which can dominate over LIV effects, especially at low redshifts, and should therefore be carefully disentangled from any extrinsic lags. Moreover, two main regimes are identified with characteristic spectral lags, corresponding to long-lasting and fast particle acceleration. Conclusions. Such intrinsic spectral lags should be detected with new-generation instruments at VHE such as the Cherenkov Telescope Array which begins operation in a few years. This will provide original constraints on AGN flare models and open a new era for LIV searches in the photon sector.

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