# Strong Gravitational Lensing by a Charged Kiselev Black Hole

## TL;DR

This paper analyzes gravitational lensing by a charged black hole surrounded by quintessence, deriving analytical solutions for light trajectories and bending angles, and exploring effects of charge and quintessence on lensing.

## Contribution

It provides new analytical solutions for null geodesics and lens equations in a charged Kiselev black hole spacetime with quintessence, extending previous uncharged models.

## Key findings

- No stable closed null orbits around the black hole.
- Charge corrections to deflection angle are negligible at large distances.
- Analytical solutions are obtained for all quintessence parameters.

## Abstract

We study the gravitational lensing scenario where the lens is a spherically symmetric charged black hole (BH) surrounded by quintessence matter. The null geodesic equations in the curved background of the black hole are derived. The resulting trajectory equation is solved analytically via perturbation and series methods for special choice of parameters and the distance of the closest approach to black hole is calculated. We also derive the lens equation giving the bending angle of light in the curved background. In the strong field approximation, the solution of the lens equation is also obtained for all values of the quintessence parameter $w_q$. For all $w_q$, we show that there are no stable closed null orbits and that corrections to the deflection angle for the Reissner-Nordstr\"om black hole when the observer and the source are at large, but finite, distances from the lens do not depend on the charge up to the inverse of the distances squared. A part of the present work, analyzed however with a different approach, is the extension of {\it Phys. Rev. D \textbf{92}, 084042 (2015)} where the uncharged case has been treated