Traversable wormholes from a smoothed string fluid in 4D Einstein-Gauss-Bonnet gravity

TL;DR

This paper shows that traversable wormholes can be sustained in four-dimensional Einstein–Gauss–Bonnet gravity using a smoothed string fluid with a radially varying equation of state. The Gauss–Bonnet coupling $\alpha$ and smoothing scale $a$ regulate throat geometry, curvature regularity, and energy-condition violations, enabling a regime where NEC violations are confined and the volume integral of exotic matter approaches zero. A Kiselev-like reinterpretation of the fluid connects a de Sitter-like core to a cosmic-string exterior, while the complexity factor and VIQ analyses demonstrate reduced structural complexity and exotic-matter requirements as $\alpha$ and $\varepsilon$ grow. Overall, the work presents a unified framework in which the same string-fluid source can generate regular black holes or stable traversable wormholes depending on the strength of higher-curvature corrections, with potential implications for viability and observations in modified gravity.

Abstract

We investigate traversable wormhole solutions in four-dimensional Einstein-Gauss-Bonnet (EGB) gravity sourced by a smoothed string fluid. Originally proposed to model regular black holes, this energy density profile is adapted here to sustain wormhole geometries by allowing for a radially varying equation of state. We obtain zero-tidal-force solutions that satisfy all traversability criteria and remain globally regular. The Gauss-Bonnet (GB) coupling $α$ plays a central role in shaping the throat geometry. We identify a parameter region ($α\geq 1$, $\varepsilon \leq 0.1$) in which the null energy condition is satisfied in the vicinity of the throat, representing a significant improvement over general relativistic counterparts. The interplay between the smoothing scale $a$ and the string density $\varepsilon$ ensures finite curvature invariants while reducing the violation of energy conditions. An analysis of the volume integral quantifier and the complexity factor further shows that strong EGB coupling simultaneously suppresses gravitational complexity and the total amount of exotic matter. These results establish a unified framework in which the same string fluid source can generate both regular black holes and stable traversable wormholes, depending on the strength of higher-curvature corrections.

Figures (8)

• Figure 1: Color gradient for the energy density $\rho(r)$ for $\varepsilon=[0,1]$, with $a=1$ and $r_0=5$.
• Figure 2: Top left panel: The geometric condition (2) $b(r)/r$, with $r_0 = 5$, $a=1$, and $\varepsilon = 0.1$. Top right panel: The geometric condition (4) for $b(r)-r b'(r)$ (flaring-out), considering the same parameters. Bottom left panel: Dependence of $b(r)/r$ on $\varepsilon$, with $r_0=5$, $a = 1$, and $\alpha=0.1$ fixed. Bottom right: Flaring-out condition $b(r) - r b'(r)$ for the same $\varepsilon$-dependent case. In the figures, the color gradient represents $\alpha \in [0,10]$ (top) and $\varepsilon \in [0,1]$ (bottom), as shown in the vertical colorbars, respectively.
• Figure 3: Left panel: Embedding profiles $z(r)$ of the wormhole in 4D EGB gravity surrounded by a smoothed string fluid, plotted for selected values of the coupling constant $\alpha$. The parameters are set to $r_0 = 5$, $a = 1$, and $\varepsilon = 0.1$. Right panel: Three-dimensional embedding diagram of the wormhole for $\alpha = 0.5$, using the same remaining parameters.
• Figure 4: Left panel: Kretschmann curvature for the wormhole in 4D EGB gravity surrounded by a smoothed string fluid, as a function of $r$. The color gradient shows the GB coupling constant in the range $\alpha \in [0,10]$ (fixed $\varepsilon=0.1$, $r_0=5$, and $a=1$). Right panel: Kretschmann curvature plotted as a color gradient for $\varepsilon \in [0,1]$, with fixed $\alpha = 0.1$, $r_0 = 5$, and $a = 1$.
• Figure 5: Radial state parameter $\omega_r(r)$ as a function of $r$, for $\alpha \in [0,10]$ (color gradient, top left panel, fixed $\varepsilon=0.1$). On the top right panel, the color gradient shows the radial state $\omega_r(r)$ for $\varepsilon \in [0,1]$ (fixed $\alpha=0.1$). Lateral state parameter $\omega_t(r)$ as a function of the coordinate $r$, for $\alpha \in [0,10]$ (bottom left panel, fixed $\varepsilon=0.1$), and for $\varepsilon \in [0,1]$ (bottom right panel, fixed $\alpha=0.1$). In all cases, we have considered $r_0 = 5.0$ and $a=1.0$.