Weak Gravitational Lensing in Dark Matter and Plasma Mediums for Wormhole-like Static Aether Solution

TL;DR

This paper investigates gravitational lensing effects caused by a wormhole-like solution in aether theory across different mediums, revealing how plasma and dark matter influence light deflection and shadow characteristics.

Contribution

It introduces a novel analysis of wormhole lensing using optical geometry and compares effects in plasma, dark matter, and non-plasma environments, including shadow behavior.

Findings

Deflection angle increases exponentially with charge.

Shadow size is smaller than Schwarzschild for r<2m.

Weak deflection angle approaches Schwarzschild behavior at infinity.

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 $\psi$ 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 $b$, $\psi$ 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 $r<2m$. At $r>2m$, the Schwarzschild is larger. As $r\to \infty$, 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.