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

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 $$\psi $$ ψ 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, $$\psi $$ ψ 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 $$r<2m$$ r < 2 m . At $$r>2m$$ r > 2 m , the Schwarzschild is larger. As $$r\rightarrow \infty $$ r → ∞ , 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.

Study of the Deflection Angle and Shadow of Black Hole Solutions in Non‐Plasma and Plasma Mediums Under the Effect of Einstein–Gauss–Bonnet Gravity

“…Any gravity theories whose limit of weak deflection is expressed as a expansion of series with a single of mass variable m can be directly addressed using the PPN framework. To the concept [64,65] the third order was investigated. One can use the space-time as…”

“…Any gravity theories whose limit of weak deflection is expressed as a expansion of series with a single of mass variable m can be directly addressed using the PPN framework. To the concept [ 64,65 ] the third order was investigated. One can use the space‐time as $$$$\begin{equation} ds^{2}=-G(r)dt^2+H(r)dr^2+r^{2}d\Omega ^{2} \end{equation}$$$$According to the third order, the coefficients of solution (31) are to be specified in the PPN series as $$$$\begin{eqnarray} G(r)&=& 1+2g_{1}(\frac{\theta }{c^{2}})+2g_{2}(\frac{\theta }{c^{2}})^{2}+2g_{3}(\frac{\theta }{c^{2}})^{3} + \cdots,\end{eqnarray}$$$$ $$$$\begin{eqnarray} H(r)&=& 1-2h_{1}(\frac{\theta }{c^{2}})+4h_{2}(\frac{\theta }{c^{2}})^{2}-8h_{3}(\frac{\theta }{c^{2}})^{3} + \cdots \end{eqnarray}$$$$where θ is a 3D Newtonian potential as …”

Weak Deflection Angle, Hawking Radiation and Greybody Bound of Reissner–Nordström Black Hole Corrected by Bounce Parameter

“…In this study, we ought to analyze such a metric under the influence of plasma and dark matter. With the shadow cast, it can also determine imprints of spacetime, and several studies were also conducted about using the black hole for dark matter detection [50,51,[59][60][61][62][63][64][65][66][67][68].…”

4D scale-dependent Schwarzschild-AdS/dS black holes: study of shadow and weak deflection angle and greybody bounding

“…In 2008, Gibbons and Werner found a new way to derive deflection angle of the black holes in weak field limits by using Gauss-bonnet theorem on the optical metric for the Schwarzschild black hole [74], then Werner extended it to stationary black holes using the Kerr-Randers optical geometry [75]. Since then, this method of Gibbons-Werner has been used in various papers to show the weak deflection angle of many black holes or wormholes in the literature [39][40][41][42][43][44][45][46][47][48][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92].…”