JCMP
Exact Asymptotically Flat TraversableWormholes in Rastall Teleparallel Gravity
Khilola Khudarganova , Shakhlo Jabbarova
We construct static, spherically symmetric traversable wormholes in the teleparallel version of Rastall gravity, in which the divergence of the matter energy-momentum tensor is tied to the gradient of the torsion scalar, ∇μΘμ = λ∂μT. Working with the non-diagonal “good” tetrad, zero tidal force and a linear radial equation of state pr = ωρ, the field equations integrate exactly. The shape function is obtained in closed parametric form; it reduces to the known power-law wormhole of general relativity when the Rastall parameter ζ → 0 and remains asymptotically flat for |ζ| < 1/2. By contrast, the diagonal tetrad yields a geometry with a solid-angle deficit, which gives an independent argument for the non-diagonal frame. Three exact results organize the physics: (i) the radial null energy condition is insensitive to the Rastall term pointwise and is violated at the throat, as flaring out demands; (ii) the strong-energy combination reduces identically to κ(ρ + pr + 2pt) = −2ζT, so it holds everywhere for ζ < 0; and (iii) the volume-integral quantifier takes the compact form IV = −2 R ∞ r s ρ ds with s = p 1 − b/r, and decreases in magnitude as ζ becomes more negative. Embedding diagrams, proper distance, anisotropy, hydrostatic equilibrium through a Rastallmodified Tolman–Oppenheimer–Volkoff equation and tidal constraints are analysed. Negative coupling reduces the exotic-matter budget near the throat and restores the strong energy condition, at the cost of the tangential dominant energy condition close to the throat for ζ ≲ −0.1.