https://doi.org/10.1140/epjc/s10052-021-09026-7
Regular Article – Theoretical Physics
Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow
MOE Key Laboratory of Artificial Micro- and Nano-structures, School of Physics and Technology, Wuhan University, 430072, Wuhan, China
Received:
18
November
2020
Accepted:
5
March
2021
Published online:
18
March
2021
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 
where b is the impact parameter and 
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.
© The Author(s) 2021
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