Globally complete non-exotic EChS wormholes

Construct globally complete five-dimensional traversable wormhole solutions in the torsionless Einstein–Chern–Simons gravity sector whose physical matter satisfies the relevant energy conditions throughout the entire exterior region r≥r₀, by solving the field equations away from the throat with appropriate matter closure conditions and boundary data.

Background

The paper establishes that, for suitable negative values of the EChS coupling αl², the physical matter can satisfy the standard pointwise energy conditions at the wormhole throat. However, the graphical analysis of the power-law family shows that several energy-condition combinations can change sign farther from the throat, so throat satisfaction does not establish a globally non-exotic wormhole.

A globally complete solution would require extending the local throat data into the asymptotic region while simultaneously solving the EChS field equations and imposing suitable matter closure conditions and boundary data. This problem is therefore a concrete unresolved extension of the paper’s local and family-specific results.

References

Several directions for future work emerge naturally from this analysis. The construction of globally complete wormhole solutions satisfying the energy conditions throughout the exterior spacetime r\geq r_0 requires solving the field equations away from the throat with appropriate matter closure conditions and boundary data.

— Non-exotic traversable wormholes in Einstein-Chern-Simons gravity  (2608.16723 - Cataldo et al., 17 Aug 2026) in Section 5, Conclusions

If a globally isotropic solution exists, it necessarily requires a non-trivial redshift function \Phi(r)\neq0, and its construction demands the integration of the resulting differential equation relating \Phi(r) and b(r), either numerically or through an appropriate ansatz.

— Non-exotic traversable wormholes in Einstein-Chern-Simons gravity  (2608.16723 - Cataldo et al., 17 Aug 2026) in Section 4.4, “Throat values as initial conditions and the isotropic pressure case”; reiterated in Section 5, Conclusions