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... order to illustrate the effect of the light bending we present its schematic view in Fig. 3. The light passing through the magnetars inclines to some θ ...
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It has been thought for decades that rotating black holes (BHs) power the energetic gamma-ray bursts (GRBs) and active galactic nuclei (AGNs), but the mechanism that extracts the BH energy has remained elusive. We here show that the solution to this problem arises when the BH is immersed in an external magnetic field and ionized low-density matter....
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... In the modern era, 29 magnetars have been discovered within our galaxy, and 2 have been found outside of it [51]. Among these, 26 have been officially classified as magnetars, while 5 are considered potential candidates [51,52]. The McGill Online Magnetar Catalog [53,54] has greatly facilitated the creation of a distribution map using the Aitoff-Hammer projection, and it is clear that magnetars align along the galactic plane, with their positions represented by black crosses in Figure 2. Table 1 shows the numerical estimate of each bending angle ∆θ ⊥ in Equation (17) for the arbitrary values r s and the magnetic fields corresponding to 24 galactic magnetars [55]. ...
... Table 1. Numerical estimation of each bending angle in Equation (17) for the arbitrary values r s and the magnetic fields corresponding to 24 galactic magnetars [52,55]. Following the notation in [21], the total bending angle caused by magnetars can be expressed in the order of the impact parameter: ...
We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields.
... Deflection angles of light in the equatorial plane are computed analytically by considering BI NED and HE theory separately. Additionally, by that the delay times due to light polarization were also calculated [12,[37][38][39][40]. ...
... In this work, we provide a comprehensive review of the post-Maxwellian parameters, their characteristics, and the underlying physics in the context of the Born-Infeld and Heisenberg-Euler theories, which are the primary frameworks within nonlinear vacuum electrodynamics. It is crucial to consider theories or calculations that align with observational results to gain insights into the nature of the geometry surrounding astrophysical black hole candidates and to assess the validity of the theory [40,42,43]. A detailed examination of the derivation and solution of the field equations based on the Born-Infeld and Euler-Heisenberg theories, as well as an exploration of the magnitudes and physical implications of the post-Maxwellian parameters within these theories, significantly contributes to the study of nonlinear electrodynamics in vacuum. ...
In this article, we provide a review of the current state of the research on the nonlinear electrodynamics of vacuum in the presence of strong electromagnetic fields. We discuss the parametrized post-Maxwellian formalism that can be facilitate calculations in the weak electromagnetic field approximation. The post-Maxwellian parameters are a set of parameters used in non-linear electrodynamics to describe the behavior of electromagnetic fields in the presence of strong fields. We also discuss the equations for the electromagnetic field in the Born-Infeld electrodynamics and in non-linear Heisenberg-Euler electrodynamics, as well as the exact solution in the form of a plane elliptically polarized wave. We represent the Lagrangian of nonlinear electrodynamics in vacuum in detail. We demonstrate that the Lagrangian can be expressed as a series of integer powers of invariants J1 and J2, which allows for the identification of nonlinear electrodynamics that are consistent with experiments carried out in a weak electromagnetic field.
We study numerically a combined gravitational and nonlinear magnetic lensing effect on electromagnetic flux. A magnetar with a dipole magnetic field and background gravitational field is considered to deflect the light rays which passed through its magnetosphere. We assume a square wave front with sides [Formula: see text][Formula: see text]m as a grid with the [Formula: see text][Formula: see text]m dynamic step. At the nodes of this grid, the rays enter perpendicularly into the cubic area, which covers the main magnetic lensing region with a magnetar at the center. On the basis of general relativity (GR) and nonlinear vacuum electrodynamics, the distribution of rays by the deflection angle in the combined field of the magnetar was obtained. On the basis of the analysis of the obtained data, it is possible to assert that the magnetic field distorts the result of gravitational lensing. Therefore, the magnetar is regarded as a gravitational-magnetic lensing object, wherein the magnetic field induces axial distortion within [Formula: see text]. These results are expected to be detectable by modern instruments.
