Gravitational deflection of charged massive particle around charged galactic wormhole

TL;DR

The paper studies the gravitational deflection of charged massive particles around a charged galactic wormhole derived from Sofue's exponential dark matter profile, extending prior light-particle results. It employs two complementary methods: the RI approach with Jacobi metric and the Gauss-Bonnet theorem in Jacobi space to obtain deflection angles; It derives the CMP Jacobi metric, the orbital equation, and computes deflection with both methods, analyzing how particle charge $q$, wormhole charge $Q$, scale $r_s$, velocity $v$, and mass $m$ influence bending, finding broadly consistent trends but quantitative differences between methods. The results suggest distinct observational signatures for charged wormholes and motivate future work connecting lensing, dark matter distributions, and tests of gravity in exotic spacetimes.

Abstract

Recently, we proposed a novel charged wormhole spacetime based on Yoshiaki Sofue's exponential dark matter density profile, referred to as the Charged Galactic Wormhole. Our previous work explored the deflection of light and massive chargeless particles in this spacetime. Building upon this foundation, we now extend our study to investigate the deflection of charged massive particles around the charged galactic wormhole, unveiling new insights and opening several promising avenues for future research. To analyze this phenomenon, we employ two distinct methodologies. The first approach utilizes the Rindler-Ishak method, leveraging the Jacobi metric to compute the particle trajectories with high precision. The second approach adopts the Gauss-Bonnet theorem, providing a geometric and topological perspective of the deflection process. A detailed comparison of the results from these two approaches is presented, highlighting their consistency and differences, along with the physical implications. This work provides deeper insights into the interaction of gravitational and electromagnetic forces around charged galactic wormholes and their influence on particle motion, contributing to the theoretical understanding of such exotic spacetime structures.

Figures (13)

• Figure 1: The orbital motion of a charged heavy particle is shown in the diagram above.
• Figure 2: The diagrams presented above illustrate the trajectory $U(\phi)$ as a function of $\phi$, for different values of $b$, $v$, and $m$ (from left to right in the upper panel) and $r_s$, $q$, and $Q$ (from left to right in the lower panel). Here, we have assumed $q>0$.
• Figure 3: The diagrams presented above illustrate the deflection angle $\alpha^{RI}$ as $b$, $v$, and $m$ dependent (from left to right in the upper panel) and $r_s$, $q$, and $Q$ dependent (from left to right in the lower panel). Here, we have assumed $q>0$.
• Figure 4: The diagrams presented above illustrate the deflection angle $\alpha^{RI}$ as $b$, $v$, and $m$ dependent (from left to right in the upper panel) and $r_s$, $q$, and $Q$ dependent (from left to right in the lower panel). Here, we have assumed $q<0$.
• Figure 5: The Gauss-Bonnet theorem is represented in the diagram on the left side. The Gauss-Bonnet theorem in connection with Riemann-Jacobi geometry is represented in the diagram on the right side.