Abstract In this paper, we construct and analyze a new class of static, spherically symmetric wormhole geometries supported by anisotropic matter distributions inspired by the Einasto density profile, which is widely used to describe dark matter haloes in galaxies. We discuss the geometrical and physical implications of such wormhole configurations through a variable redshift function in the context of general relativity. Within this model, a number of physical constraints are taken into consideration, including energy conditions (like the null energy condition) and the conservation equation, which bring critical checks on the viability of traversable configurations. We further discuss the EoS parameter, the behavior of the anisotropy factor, and the exoticity parameter, all of which, taken together, determine the matter content supporting the wormhole throat. In this respect, we present the active gravitational mass function along with the embedding diagram in order to better visualize the geometrical properties of the considered wormhole. For completeness, we then consider the Kretschmann scalar, which characterizes the geometrical properties and verifies the absence of singularities in the whole domain. We also analyze the complexity factor associated with the matter distribution to give an indication about the internal structure and gravitational behavior of the wormhole. The impact of the Einasto profile on such physical and geometrical quantities is emphasized, showing that dark matter-inspired models for the density can rightfully minimize the amount of exotic matter within this class of traversable wormholes. Indeed, this formally demonstrates that the framework here considered does provide physically acceptable solutions that are asymptotically flat and points towards the fundamental contribution of dark matter distributions in the building-up of stable wormhole geometries.
Albalahi et al. (Wed,) studied this question.