Noncommutative geometry-inspired wormholes supported by quasi-de Sitter and Chaplygin-like equations of state

TL;DR

This paper develops a framework for constructing regular, traversable wormholes inspired by noncommutative geometry, using specific equations of state to control exotic matter distribution and spacetime properties.

Contribution

It introduces a unified approach employing quasi-de Sitter and Chaplygin-like equations of state to engineer wormholes with localized exotic matter and controlled redshift effects.

Findings

Wormholes with regular shape functions and confined exotic matter are achievable.

Redshift functions influence the distribution and nature of exotic matter near the throat.

Chaplygin-like EOS allows for tunable anisotropies and local blueshift regions.

Abstract

We construct static, spherically symmetric wormhole solutions with a nontrivial redshift function, inspired by noncommutative geometry, in which point sources are replaced by Gaussian smearing of minimal length, yielding a regular shape function. Within this framework, we derive model-independent relations that isolate the role of the redshift function in controlling the stress-energy components and the violation of the null energy condition (NEC). Negative or suitably tuned redshifts confine the exotic matter to a thin neighborhood of the throat. We then reformulate this redshift engineering in matter terms through a quasi-de Sitter equation of state (EOS) with localized Gaussian or Lorentzian perturbations, obtaining minimally exotic wormholes that are regular, horizon-free, and asymptotically flat. Finally, we extend the analysis to a Chaplygin-like EOS, introducing a nonlinear coupling between pressure and density that yields redshift wells with possible local blueshift regions and tunable anisotropies governed by a certain nonlinearity parameter. Together, these results provide a unified and physically transparent framework for constructing traversable noncommutative-geometry-inspired wormholes with controlled, spatially localized exotic matter content.