Anisotropic fuzzy wormholes in Einstein gravity: A study with Einasto dark matter model

We construct a class of static, spherically symmetric fuzzy wormhole (WH) solutions in Einstein gravity by deriving an analytic shape function (SF) sourced by the Einasto dark matter density profile. The metric includes a global monopole parameter and a constant redshift function, and the SF is obtained by integrating the Einstein field equations (EFEs) with the Einasto profile. We verify the geometric requirements for a traversable WH by checking the throat condition and the flare-out constraint, and illustrate the behavior of related diagnostic combinations graphically for representative parameter choices. Using the derived matter components, we perform a comprehensive physical analysis. The energy condition (EC) diagnostics show that the null and weak ECs are generically violated near the throat (indicating the presence of exotic matter) while the dominant EC is partially satisfied in outer regions. The active gravitational mass is found to be slightly negative near the throat, consistent with exotic supporting matter, but becomes positive and increases with radius and the Einasto index. Tolman–Oppenheimer–Volkoff (TOV) equilibrium analysis reveals that hydrostatic and anisotropic forces can counterbalance, suggesting possible static stability for chosen parameter sets. The anisotropy parameter remains positive in the domain studied, providing a repulsive contribution that helps sustain the throat. Finally, the complexity factor (CF) [Formula: see text] peaks near the throat and asymptotically vanishes ([Formula: see text] as [Formula: see text]), indicating that the model localizes structural complexity to the inner region while approaching simpler behavior at large radii, and also volume integral quantifier (VIQ) is used to evaluate the total amount of exotic matter (EM). These results together indicate that Einasto profile induced SFs offer physically rich fuzzy WH configurations in Einstein gravity, with exotic effects confined mainly to the throat region and improved physical behavior at larger distances.