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A 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 $(1-b_c/b)$ where $b$ is the impact parameter and $b_c$ 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 $l$ increase 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.
The gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds $pi$, gravitational lensing can be analytically approximated by the so-called strong deflection limit
A modified Hayward black hole is a nonsingular black hole. It is proposed to form when the pressure generated by quantum gravity can stop matters collapse as the matter reaches Planck density. Strong deflection gravitational lensing happening nearby
In this article, we present an overview of the new developments in problems of the plasma influence on the effects of gravitational lensing, complemented by pieces of new material and relevant discussions. Deflection of light in the presence of gravi
Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono, Kitamura, Asada, Phys. Rev. D {bf 94}, 084015 (2016) ], we discuss a method of calculating the bending angle of light in a static, spherically symmetric and asymptotically fl
Strong field gravitational lensings are dramatically disparate from those in the weak field by representing relativistic images due to light winds one to infinity loops around a lens before escaping. We study such a lensing caused by a charged Galile