Dynamical Structure of Einasto Dark Matter Wormholes: Thin-Shell Stability and Particle Transitions

Abstract

In this manuscript, we develop topologically charged static and spherically symmetric wormhole (WH) configurations in Einstein gravity by employing the Einasto dark matter profile to construct an analytic shape function. The resulting spacetime satisfies the fundamental traversability conditions, while the matter sector exhibits localized violations of energy conditions near the throat, indicating confined exotic matter content. We analyze equilibrium through the TOV framework, revealing a non-equilibrium force competition in which hydrostatic and anisotropic contributions self-organize to sustain static configurations within specific parameter domains. Stability is examined via the anisotropy parameter and further extended to linearized radial perturbations of the surrounding shell, uncovering parameter-dependent stability windows that characterize the system's nonlinear response. A detailed dynamical analysis shows that the monopole charge parameter significantly restructures the effective potential landscape, modifying curvature and inducing qualitative transitions in particle motion. The coupled interplay between monopole charge, angular momentum, and particle energy governs a nonlinear transition from tightly wound quasi-bound states to unbounded scattering trajectories. This transition reflects an emergent dynamical phase structure in the WH spacetime. Furthermore, the complexity factor exhibits strong localization near the throat and vanishes asymptotically, indicating that structural complexity is confined to the inner nonlinear regime, whereas a volume integral quantifier is employed to estimate the total exotic matter content required to sustain the configuration.