Gravitational lensing due to charged galactic wormhole

TL;DR

This work addresses gravitational lensing by a charged galactic wormhole formed within a realistic dark matter distribution, using backreaction in Einstein–Maxwell theory with the exponential profile $\rho^{w}=\rho_s e^{-r/r_s}$. The authors derive a self-consistent metric with a shape function $b(r)$ and an effective function $b_{eff}(r)=b(r)-\frac{Q^2}{r}$, analyze embedding and NEC stability, and compute photon deflection and image formation in both strong-field and Jacobi-metric contexts. They show a photon sphere at $r_m=\sqrt{2}\,Q$ and obtain a strong-field lensing form $\alpha(r_0)=-a\log\left(\frac{r_0}{r_m}-1\right)+b_R+b_D-\pi+O(r_0-r_m)$, while for massive particles the RI and GB methods converge as $v\to1$, with deflection depending on $b$, $v$, and $r_s$. The results predict observational lensing signatures such as multiple Einstein rings and velocity/charge-dependent effects, offering a framework to probe dark matter–spacetime interactions with future facilities like JWST, ALMA, or gravitational-wave detectors.

Abstract

We propose the back reaction to the charged galactic wormhole spacetime based on Yoshiaki Sofue's exponential dark matter density profile to find exact solutions. The charges act as an additional component to the static wormhole, which is primarily formed by the galactic dark matter density. Unlike traditional mass-based models, this solution incorporates charge effects within a realistic dark matter distribution, revealing unique interactions between dark matter, electromagnetic fields, and spacetime curvature. This study confirms the criteria for wormhole formation, designating it the "Charged Galactic Wormhole," and offers a new framework for investigating galactic structures, with potential observational signatures that deepen our understanding of dark matter and spacetime. Later, the proper radial distance and the embedding surface were also analyzed. Furthermore, the deflection of light around a charged galactic wormhole was investigated, along with a comprehensive review of the resulting image. The deflection of massive objects (charge less) near charged galactic wormholes is studied using the Gauss-Bonnet and Rindler-Ishak methods, with a detailed comparison of the results from both approaches. Additionally, in both the Rindler-Ishak (RI) and Gauss-Bonnet (GB) methods, when v tends to 1 i.e. when particle's velocity comparable to the speed of light , the results from these approaches converge, producing the same outcome as strong gravitational lensing.

Figures (14)

• Figure 5: The above diagrams are the graphical representation of embedding surface $z(r)$ and radial distance $l(r)$ that correspond considering the criteria $Q=1$, $\rho_0=0.00003$ and $r_s=1$. .
• Figure 6: The above diagram is the full visualizing of the charged wormhole.
• Figure 7: The above diagrams are the graphical representation of the lensing coefficients $\bar{a}$, $\bar{b}$ and $\bar{u_m}$ as functions of parameter $Q$ (left part) and deflection angle $\alpha(r_0)$ in relation to the closest approach distance $(r_0)$ for various values of $Q$ (right part).
• Figure 8: The above diagrams are the graphical representation of the deflection angle $\alpha(\theta)$ in relation to $\theta$ for various values of $Q$ (left part) and the deflection angle $\alpha(\theta)$ in relation to $Q$ for various values of $\theta$ (right part).
• Figure 9: The above diagram is the graphical representation of $\widehat{\alpha}$ and $\theta-\beta$ expressed as $\theta$ dependent and also $-\widehat{\alpha}$ and $-\theta-\beta$ expressed as $-\theta$ dependent, assuming $Q=1$ and $\beta=0$ is illustrated via a direct path with dots that goes via the origin.Also the dashed lines are applied to represent $\theta(\theta)-\beta(\theta)$ and $-\theta(-\theta)-\beta(-\theta)$, assuming $\beta=0.40 arcseconds$