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

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.

Figures (12)

• Figure 1: Plot of the metric coefficient $g^{xx} = f(x)$, as defined in \ref{['fx']}. The extremal case occurs at $\mu = \mu_e = 1.9041\ldots$ (solid line), where two coinciding throats are located at $x_e =3.0224\ldots$. For $\mu > \mu_e$, a non-extremal wormhole with two distinct throats is present (dotted line shown for $\mu = 2.3$). For $\mu < \mu_e$, the absence of throats indicates that the gravitational object is not a wormhole (dashed line shown for $\mu = 1.3$).
• Figure 2: Embedding diagram for the noncommutative wormhole with $\mu = 1.95$, shown in comparison to the corresponding Morris--Thorne wormhole (dashed line), as viewed in profile. To obtain the full three-dimensional geometry, the diagram must be revolved around the vertical $\widetilde{z}$-axis.
• Figure 3: Left panel: Radial pressure $p_r$ plotted as a function of the rescaled radial variable $x$ for $\mu = 1.905$, and various values of $\Phi_0$ in the type I redshift function $\Phi$ (see Table \ref{['table:Phi']}). The case $\Phi_0 = 0$ is shown as a solid line; $\Phi_0 = 1$ as a black dashed line; $\Phi_0 = 5$ as a black spacedotted line; $\Phi_0 = -1$ as a red dashed line; and $\Phi_0 = -5$ as a red spacedotted line. Central panel: Tangential pressure $p_t$ plotted against $x$ for the same set of parameters and line styles as in the left panel. Right panel: NEC represented against $x$ for the same set of parameters and line styles as in the left panel.
• Figure 4: Left panel: Radial pressure $p_r$ plotted as a function of the rescaled radial variable $x$ for $\mu = 1.905$, and various parameter triples $(\Phi_0, n, k)$ used in the type II redshift function $\Phi$ (see Table \ref{['table:Phi']}). The reference case $\Phi_0 = 0$ is shown as a solid line. The triple $(\pm 1, 2, 1)$ is represented by dashed lines (positive $\Phi_0$ in red), $(\pm 1, 4, 2)$ by spacedotted lines (positive in red), $(\pm 1, 1, 1/2)$ by dash-dotted lines (positive in red), and $(\pm 5, 3, 1)$ by spacedashed lines (positive in red). Central panel: Tangential pressure $p_t$ plotted against $x$ for the same parameters, triples, and line styles as in the left panel. Right panel: NEC represented against $x$ for the same set of triples and line styles as in the left panel.
• Figure 5: Left panel: Radial pressure $p_r$ plotted as a function of the rescaled radial variable $x$ for $\mu = 1.905$, and various values of $\Phi_0$ used in the type III redshift function $\Phi$ (see Table \ref{['table:Phi']}). The case $\Phi_0 = 0$ is shown as a solid line, $\Phi = 1$ as a dashed line, $\Phi_0 = 5$ as a spacedotted line, $\Phi_0 = -1$ as a red dashed line, and $\Phi_0 = -5$ as a red spacedotted line. Central panel: Tangential pressure $p_t$ plotted against $x$ for the same choices of $\Phi_0$ and line styles as in the left panel. Right panel: NEC represented against $x$ for the same set of values of $\Phi_0$ and line styles as in the left panel.