Deflection of light by dark matter supporting traversable wormholes in the framework of Kalb-Ramond gravity

TL;DR

This work investigates asymptotically flat traversable wormholes supported by galactic dark matter halos within Kalb-Ramond gravity, using King and Navarro-Frenk-White density profiles. By solving the KR-modified Einstein equations with a constant redshift function, it derives shape functions Ω(r) that satisfy throat and flare-out conditions and yield asymptotic flatness. The analysis reveals that the radial null energy condition at the throat depends on the KR parameter λ, allowing either exotic or nonexotic matter to sustain the wormholes, while other energy conditions are largely satisfied within parameter ranges. The study also examines embedding, complexity, active gravitational mass, total gravitational energy, and strong-field lensing, showing a diverging deflection angle near the throat and a vanishing angle far away, highlighting potential observational signatures of such KR-supported wormholes.

Abstract

This study explores the possible formation of asymptotically flat traversable wormholes within dark matter halos under the framework of Kalb-Ramond gravity. The wormhole solutions are derived based on the King and Navarro-Frenk-White dark matter density profiles associated with anisotropic matter sources. For a particular set of parameters, the proposed shape functions are found to be positively increasing and satisfy all the essential geometric conditions along with the flare-out condition, thereby supporting asymptotically flat traversable wormholes. To study the underlying matter content responsible for the wormhole structures, we analyze the null energy condition at the wormhole throat and provide graphical representations of various energy conditions, highlighting both the regions where they are satisfied and where they are violated. The stability of the reported wormhole solutions is confirmed through the generalized Tolman-Oppenheimer-Volkoff equation. In addition, we explore several physical features of the wormhole configurations, including the embedding surface, complexity factor, active gravitational mass, and total gravitational energy. Moreover, we investigate the deflection of light by these wormholes, finding that the deflection angle approaches zero at large distances, where the wormhole's gravity is negligible, and diverges near the throat, where the gravitational influence is extremely strong.

Figures (15)

• Figure 1: Shows the radial variations of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) under the King DM model with $\alpha$ = 1.5, $r_s = 0.3$, $r_0 = 1$, $\beta$ = 1, and $\eta$ = -3/2.
• Figure 2: Shows the radial variations of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) under the King DM model with $\alpha$ = 1.5, $r_s = 0.3$, $r_0 = 1$, $\beta$ = 1, and $\lambda$ = 1.
• Figure 3: Shows the radial variations of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) under the NFW DM model with $\rho_s$ = 0.005, $r_s = 2.1$, $r_0 = 1$, and $\gamma$ = 2.
• Figure 4: Shows the radial variations of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) under the NFW DM model with $\rho_s$ = 0.005, $r_s = 2.1$, $r_0 = 1$, and $\lambda$ = 1.
• Figure 5: Shows the valid region$^{({\color{orange}*})}$ and invalid region$^{({\color{blue}*})}$ for $\rho(r)$ (Left), $\rho(r)+P_r(r)$ (Middle), $\rho(r)+P_t(r)$ (Right) in the above panel, and $\rho(r)-P_r(r)$ (Left), $\rho(r)-P_t(r)$ (Middle), $\rho(r)+P_r(r)+2P_t(r)$ (Right) in the below panel under the King DM model with $\alpha$ = 1.5, $r_s = 0.3$, $r_0 = 1$, $\beta$ = 1, and $\eta$ = -3/2.