Yukawa-Casimir wormholes within Einstein-Cartan gravity framework

TL;DR

This paper demonstrates that traversable wormholes supported by Yukawa-Casimir energy densities can be realized within Einstein-Cartan gravity by incorporating spin-torsion via Weyssenhoff fluid. Three explicit density profiles yield analytic/semi-analytic shape functions Ω(r) that satisfy the flare-out and throat conditions but require exterior Schwarzschild matching due to non-asymptotic flatness; energy conditions near the throat are violated, quantified by the VIQ which remains negative close to r0 and vanishes at the throat in the relevant Λ range. Equilibrium is achieved through a balance of gravitational, hydrostatic, and anisotropic forces in the TOV framework, with tidal constraints and embedding distances indicating traversability is feasible. The analysis of shadows and strong deflection shows distinctive lensing signatures that depend on the redshift parameter α and the EC cosmological constant Λ, supporting the physical plausibility of Yukawa-Casimir wormholes in EC gravity and motivating further explorations in modified gravity contexts.

Abstract

The Einstein-Cartan (EC) theory of gravity provides a natural extension of general relativity by incorporating spacetime torsion to account for the intrinsic spin of matter. In this work, we investigate Yukawa-Casimir traversable wormholes supported by three distinct Yukawa-Casimir energy density profiles within the framework of EC gravity. The resulting shape functions are shown to satisfy all the fundamental requirements for traversable wormhole geometries. Our analysis reveals that the presence of exotic matter is unavoidable in sustaining these wormholes, and we quantify its total amount through the volume integral quantifier. Furthermore, the equilibrium of the wormhole configurations is established by examining the Tolman-Oppenheimer-Volkoff equation. To enhance the physical relevance of the present work, we study several key features of the wormholes, including the embedding surface, proper radial distance, tidal forces, and total gravitational energy. In addition, we analyze the optical properties of wormholes by examining both the shadow and the strong deflection angle. All the findings collectively demonstrate the physical plausibility of Yukawa-Casimir traversable wormholes within the EC gravity framework.

Figures (15)

• Figure 1: Depiction of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) against the radial coordinate $r$ for the energy density model-I with parameters $r_0 = 0.75 km$, $\alpha = -0.8 km$, $S_0 = 0.01 km^{-1}$, and $\lambda = 1.45km^{-1}$.
• Figure 2: Depiction of the 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 the energy density model-I with parameters $r_0 = 0.75 km$, $\alpha = -0.8 km$, $S_0 = 0.01 km^{-1}$, and $\lambda = 1.45km^{-1}$.
• Figure 3: Depiction of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) against the radial coordinate $r$ for the energy density model-II with parameters $r_0 = 0.75 km$, $\alpha = -0.8 km$, $S_0 = 0.01 km^{-1}$, $\lambda = 1.45km^{-1}$, $\mu = 1 km^{-1}$, and $\nu = 1$.
• Figure 4: Depiction of the 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 the energy density model-II with parameters $r_0 = 0.75 km$, $\alpha = -0.8 km$, $S_0 = 0.01 km^{-1}$, $\lambda = 1.45km^{-1}$, $\mu = 1 km^{-1}$, and $\nu = 1$.
• Figure 5: Depiction of the shape function $\Omega(r)$ (Left), $\Omega(r)/r$ (Middle), $\Omega'(r)$ (Right) against the radial coordinate $r$ for the energy density model-III with parameters $r_0 = 0.75 km$, $\alpha = -0.8 km$, $S_0 = 0.01 km^{-1}$, $\lambda = 1.45km^{-1}$, $\nu$ =0.4, and $\beta = 1km^{-1}$.