Effect of power-law Maxwell field to the gravitational lensing

Gürtuğ, Özay; Mangut, Mert

doi:10.1103/physrevd.99.084003

Cited by 15 publications

(22 citation statements)

References 38 publications

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“…Therefore, the angle between two coordinate directions d and δ is given by the invariant formula (see Figure 1 in ref. [])

\cos (ψ) = \frac{d^{i} δ_{i}}{\sqrt{((), d^{i}, d_{i}) ((), δ^{j}, δ_{j})}} = \frac{g_{i j} d^{i} δ^{j}}{\sqrt{((), g_{i j}, d^{i}, d^{j}) ((), g_{k l}, δ^{k}, δ^{l})}}

…”

Section: Bending Of Light In Nonlinear Electrodynamicsmentioning

confidence: 99%

“…This solution corresponds to the undeflected light in the absence of gravity, (see Figure 1 in ref. [], it is displayed as a solid horizontal line ). The next step is to substitute the first order homogeneous solution to the right‐hand side and solve for the full inhomogeneous equation which admits the approximate solution as

\begin{matrix} true \\ right u & = & left \frac{1}{r} = \frac{\sin φ}{R} + \frac{M}{R^{2}} ({} \cos^{2} φ + 1) \\ left + \frac{q^{2}}{4 R^{3}} ({} 3 φ \cos φ - \sin φ [2 - \cos^{2} φ]) \\ left + \frac{q^{3} b}{30 R^{4}} ({} \cos^{2} φ [6 - \cos^{2} φ] + 3) . \end{matrix}

We differentiate Equation with respect to φ, in accordance with Equation to get

A (r, φ)

\begin{matrix} true \\ right A false(r, φ false) & = & left - \frac{r^{2}}{R} \cos φ - \frac{r^{2}}{R^{2}} ({M \sin 2 φ + \frac{q^{2}}{4 R} [2 \cos^{2} φ - \sin^{2} φ) \\ left (} - 3 φ \sin φ] + \frac{q^{3} b}{15 R^{2}} [\sin 2 φ (() \cos^{2} φ - 3)]) . \end{matrix}

The constant parameter R is called the impact parameter and it is related to the physically meaningful area distance

r_{0}

of closest approach that occurs when

φ = π / 2

, which yields <...>…”

Section: Bending Of Light In Nonlinear Electrodynamicsmentioning

confidence: 99%

“…When this result is compared with the linear Maxwell case (Equation (28) in ref. []), it is observed that in addition to the first three terms on the right hand side, there is an additional term which is associated with a nonlinearity parameter b . In the case of positive charge, the closest approach distance decreases as long as the nonlinearity parameter b increases.…”

Section: Bending Of Light In Nonlinear Electrodynamicsmentioning

confidence: 99%

“…The value of this angle is measured relative to the coordinate planes where

φ =

constant (see Figure 1 in ref. []). For the small bending angle,

\tan ψ_{0} \approx ψ_{0}

.…”

Section: Bending Of Light In Nonlinear Electrodynamicsmentioning

confidence: 99%

“…If this huge amount of charge is assumed to be at rest, then the produced electric field in the surrounding region becomes very high. In such a scenario, the bending angle of light is considered in our recent study in a power law NED model together with the cosmological constant. It has been shown that the bending angle is affected by the value of the power parameter k of the Lagrangian

L = - α {scriptF}^{k}

.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Gravitational Lensing in a Model of Nonlinear Electrodynamics: The Case for Electrically and Magnetically Charged Compact Objects

Gürtuğ

Mangut

2020

Annalen der Physik

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The astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated. Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coincide with the linear case and it becomes hard to identify the effect of nonlinearity. However, the calculation of the redshift has shown that while the increase in the electric field leads to a decrease in the gravitational redshift,the presence of the strong magnetic field contributes to the gravitational redshift in an increasing manner.

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“…Therefore, the angle between two coordinate directions d and δ is given by the invariant formula (see Figure 1 in ref. [])