Eur. Phys. J. C (2022) 82: 1057
https://doi.org/10.1140/epjc/s10052-022-11030-4

Regular Article - Theoretical Physics

Weak gravitational lensing in dark matter and plasma mediums for wormhole-like static aether solution

¹ Division of Science and Technology, Department of Mathematics, University of Education, 54590, Lahore, Pakistan
² Physics Department, De La Salle University, 2401 Taft Avenue, 1004, Manila, Philippines
³ Physics Department, Eastern Mediterranean University, via Mersin 10, 99628, Famagusta, North Cyprus, Turkey
⁴ Physics Department, Mapúa University, 658 Muralla St., 1002, Intramuros, Manila, Philippines

^d ali.ovgun@emu.edu.tr

Received: 22 July 2022
Accepted: 12 November 2022
Published online: 23 November 2022

Abstract

In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma, and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss–Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behavior of the bending angle with respect to the impact parameter b, mass m as an integration constant, and parameter q in non-plasma and plasma mediums. We examine that the deflection angle is exponentially increasing as direct with charge. Also, we observe that for small values of b, increases, and for large values of b the angle decreases. We also considered analysis to the shadow cast of the wormhole relative to an observer at various locations. Comparing it the Schwarzschild shadow, shadow cast is possible for wormhole as . At , the Schwarzschild is larger. As , we have seen that the behavior of the shadow, as well as the weak deflection angle, approaches that of the Schwarzschild black hole. Overall, the effect of plasma tends to decrease the value of the observables due to the wormhole geometry.