Non-exotic traversable wormholes with strong deflection angle in King and Dekel-Zhao dark matter halos under f(R,Lm) gravity

TL;DR

This work demonstrates that asymptotically flat traversable wormholes supported by non-exotic matter can exist within King and Dekel-Zhao dark matter halos in $f(R,L_m)$ gravity. By employing two gravity–matter couplings, Model-I $f(R,L_m)=\frac{R}{2}+L_m^{\alpha}$ and Model-II $f(R,L_m)=\frac{R}{2}+(1+\lambda R)L_m$, the authors derive wormhole solutions with DM-halo density profiles, obtain shape functions, and verify energy conditions indicating absence of exotic matter. They further analyze embedding surfaces, total gravitational energy, and the strong deflection angle to assess traversability and gravitational-lensing signatures, finding repulsive gravity behavior and observable lensing features near the throat. The results suggest that the interplay between modified gravity and DM halos can yield physically viable, non-exotic wormholes with potentially characteristic observational footprints in gravitational lensing.

Abstract

In this article, we investigate asymptotically flat non-exotic traversable wormhole geometries within the King and Dekel-Zhao dark matter halos in the framework of $f(R, L_m)$ gravity. Two functional forms of the theory are considered: Model-I: $f(R, L_m)=(R/2) + L_m^α$ and Model-II: $f(R, L_m)=(R/2) + (1 + λR)L_m$. For both models, wormhole solutions are obtained and analyzed using the King and Dekel-Zhao dark matter density profiles, allowing us to explore how the underlying matter distribution influences the wormhole structures. The energy conditions are examined to verify the feasibility of sustaining the wormhole geometries with non-exotic matter, while embedding surfaces, proper radial distance, and total gravitational energy are studied to illustrate the wormhole's physical viability and traversability. Moreover, we test the strong deflection angle and its implications for gravitational lensing and show possible observational signatures of such wormhole configurations. Our results indicate that within $f(R, L_m)$ gravity, and for appropriate parameter choices, dark matter environments can sustain physically consistent non-exotic traversable wormhole geometries with distinct gravitational lensing signatures, providing new insights into the interplay between modified gravity, dark matter, and astrophysical observations.

Figures (12)

• Figure 1: Shows the characteristics of shape function $\xi(r)$ (Left), the ratio $\xi(r)/r$ (Middle), and the derivative $\xi'(r)$ (Right) against the radial coordinate $r$ for King DM model under the $f(R, L_m)$ gravity model-I with parameters $\beta= 0.65$, $\gamma = 1$, $\eta = -0.5$, $r_s$ = 1.01, and $r_0 = 1.4$.
• Figure 2: Shows the characteristic of energy density $\rho(r)$ (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 for King DM model under the $f(R, L_m)$ gravity model-I with parameters $\beta= 0.65$, $\gamma = 1$, $\eta = -0.5$, $r_s$ = 1.01, and $r_0 = 1.4$.
• Figure 3: Shows the characteristics of shape function $\xi(r)$ (Left), the ratio $\xi(r)/r$ (Middle), and the derivative $\xi'(r)$ (Right) against the radial coordinate $r$ for Dekel-Zhao DM model under the $f(R, L_m)$ gravity model-I with parameters $\rho_s= 0.06$, $\kappa = 2.12$, $r_s$ = 6, and $r_0 = 1.4$.
• Figure 4: Shows the characteristic of energy density $\rho(r)$ (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 for Dekel-Zhao DM model under the $f(R, L_m)$ gravity model-I with parameters $\rho_s= 0.06$, $\kappa = 2.12$, $r_s$ = 6.5, and $r_0 = 1.4$.
• Figure 5: Shows the characteristics of wormhole shape function $\xi(r)$ (\ref{['B3']})(Left), the function $\xi(r) - r$ (Left-Middle), the ratio $\xi(r)/r$ (Right-Middle), and the derivative $\xi'(r)$ (Right) against the radial coordinate $r$ under the $f(R, L_m)$ gravity model-II with parameter $r_0 = 1.4$.