Rotating Traversable Wormholes with a Throat-Localized Conical Dressing and Two Conical Cosmic-String Cores

Abstract

A stationary axisymmetric traversable wormhole with a throat-localized conical factor is developed. The conical factor produces two genuine conical tips at the poles of each angular cross-section, interpreted as cosmic-string cores along the rotation axis. A single consistent background geometry is used throughout. The metric is written in proper radial distance \(l\), and the exact radial null-energy-condition (NEC) is derived and evaluated at the throat. It is shown that the ideal string cores saturate, rather than violate, the radial NEC, so the required exoticity is supplied by the smooth throat sector together with the localized dressing. Scalar perturbations are then studied on the same background. The exact axisymmetric sector, its Schr\"odinger form, and the coupled nonaxisymmetric system generated by the localized conical dressing are obtained. Numerical results show that NEC violation is throat-centered, while the clearest dynamical signature of the dressed throat is nonaxisymmetric angular-channel mixing.