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 Schrödinger 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.

Figures (12)

• Figure 1: Exact radial null-energy-condition profile $8\pi G\,N_{\pm}(l)$ for the corrected rotating traversable wormhole with localized conical dressing. The NEC is most strongly violated at the throat $l=0$, where the exact value is determined by the sum of the smooth wormhole contribution and the defect-dressing correction. Away from the throat, the profile relaxes toward zero, showing that the exoticity is localized rather than global.
• Figure 2: Exact effective potential $V_{\ell 0}(x)$ for the axisymmetric scalar sector. The potential is smooth and throat-centered, and its height increases with $\ell$, producing progressively stronger barriers for scalar-wave transmission through the wormhole throat.
• Figure 3: Transmission coefficient $T_{\ell 0}(\sigma)$ for axisymmetric scalar perturbations. Lower-frequency waves are more strongly reflected by the throat-centered barrier, while higher-frequency waves are transmitted more efficiently. Increasing $\ell$ shifts the transmission onset to higher frequencies, consistent with the higher effective potential barrier.
• Figure 4: Constant-deficit benchmark angular eigenvalues $\Lambda_{nm}$ as functions of the conical parameter $\alpha_{0}$. A uniform conical defect shifts the angular spectrum, with the effect becoming stronger for larger $|m|$. This benchmark isolates the purely conical spectral shift in the separable model and provides a control comparison for the localized dressed-throat case.
• Figure 5: Angular coupling matrix $C^{(1)}_{j\ell}$ for the $m=1$ sector. The matrix displays a structured pattern of diagonal and off-diagonal couplings, showing that the localized dressed-throat model induces nontrivial channel mixing rather than a simple uniform spectral shift.