Traversable Wormholes induced by Thomas-Fermi energy density

TL;DR

This paper constructs and analyzes traversable wormhole solutions supported by dark matter profiles, especially the Thomas-Fermi distribution, ensuring physical plausibility and geometric consistency.

Contribution

It introduces a systematic method to build wormholes supported by realistic dark matter distributions, reformulating Einstein equations in terms of matter variables.

Findings

Explicit wormhole solutions with Thomas-Fermi dark matter profiles.

Conditions for horizon absence and flare-out are satisfied.

Framework for analyzing matter distribution independently of metric functions.

Abstract

We investigate spherically symmetric and static traversable wormholes supported by exotic matter, focusing on solutions sourced by physically motivated dark matter energy density profiles. Considering the Thomas-Fermi-type distribution, we construct explicit forms of the shape function $b(r)$ and analyze the resulting radial and tangential pressures, carefully addressing the requirements of the flare-out condition at the throat and the absence of horizons. We explore zero-tidal-force configurations as well as inhomogeneous equations of state, demonstrating how appropriate choices of the radial pressure allow for finite and well-behaved redshift functions throughout the spacetime. Boundary conditions at a finite radius are implemented to ensure vanishing energy density and pressures, and asymptotic expansions are derived to characterize the behavior of the metric and matter content near the edge of the dark matter halo. Additionally, we reformulate the Einstein field equations entirely in terms of the energy density, radial and tangential pressures, and their derivatives, providing a framework to analyze the matter distribution independently of the explicit metric functions. Our results offer a systematic methodology to construct physically consistent wormhole geometries supported by realistic dark matter halos, highlighting the intricate interplay between matter profiles, equations of state, and geometric constraints.