Non-exotic traversable wormholes in Einstein-Chern-Simons gravity
We investigate traversable wormhole solutions in five-dimensional Einstein-Chern-Simons (EChS) gravity, a gauge-theoretic extension of General Relativity that introduces a higher-curvature correction parametrized by the combination $αl^2$, where $α$ is a dimensionless coupling and $l$ is a length scale. Working with the Morris-Thorne metric and an anisotropic fluid, we derive exact expressions for the energy density, radial pressure, and lateral pressure at the wormhole throat. We show that the radial Null Energy Condition (NEC) is satisfied at the throat if and only if $αl^2\leq-r_0^2$, being saturated at $αl^2=-r_0^2$ and strictly satisfied for $αl^2<-r_0^2$, independently of the shape function. In the latter regime, the energy density is strictly positive and the full NEC, Weak, Strong, and Dominant Energy Conditions can be simultaneously satisfied. These results are established analytically for arbitrary shape functions and illustrated concretely for the power-law family $b(r)=r_0(r_0/r)^n$, $Φ=0$, for which all four standard energy conditions are satisfied at the throat for all $n>0$ when the EChS coupling is sufficiently negative. We further show that the radial pressure is negative and geometrically fixed at the throat, independently of $α$, $b(r)$, and $Φ(r)$. Using the Volume Integral Quantifier (VIQ), we establish that the EChS correction reduces the magnitude of the negative integrated NEC contribution relative to GR, and derive an exact closed-form critical coupling $αl^2_{\rm crit}$ at which the VIQ vanishes. The hierarchy $αl^2_{\rm crit}<-r_0^2<0$ shows that NEC satisfaction at the throat and a non-negative global VIQ are compatible but distinct conditions, both achievable within EChS gravity. All results reduce continuously to those of GR in the limit $l\to0$, confirming the consistency of the framework.