Lorentz Symmetry Breaking Traversable Wormhole Models Supported by Einasto Dark Matter

Abstract

We investigate static, spherically symmetric traversable wormholes in Kalb Ramond gravity, where spontaneous Lorentz symmetry breaking arises from a non-vanishing vacuum expectation value of the antisymmetric Kalb Ramond field. The matter sector is modeled by the Einasto dark matter density profile, yielding an analytical shape function expressed via the incomplete Gamma function. The resulting geometry satisfies the throat, flare-out, and asymptotic-flatness requirements, with embedding diagrams providing a geometric visualization of the wormhole structure. The energy density stays positive throughout the considered domain, while the radial null energy condition is violated near the throat, showing that the exotic matter required for traversability can be localized to a restricted region. The internal structure is further characterized through the complexity factor, which is most pronounced near the throat and gradually decays to zero at larger radii. We also examine the total gravitational energy, active gravitational mass, average pressure, and equilibrium behavior via the generalized TOV equation and pressure anisotropy; for the constant-redshift configuration, equilibrium is maintained by a balance between the hydrostatic and anisotropic forces. The optical properties of the spacetime are further explored through the photon sphere, critical impact parameter, light deflection angle, and echo time. Finally, the volume integral quantifier is used to estimate the total amount of null-energy-condition-violating matter, showing that the exotic contribution remains concentrated near the wormhole throat. The analysis highlights the combined role of the Kalb Ramond gravitational parameter and the Einasto matter distribution in shaping the geometric, energetic, and observational characteristics of the resulting wormhole configurations.