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arXiv2026

Scalar halos and conical matching for finite-width vortices at a wormhole throat

We study the static matter constraint associated with a conical deficit that varies along a string near a wormhole throat. A positive scalar-dependent factor multiplying the complete Abelian-Higgs Lagrangian couples a finite-width vortex to a canonical kink. At critical coupling, we obtain the leading longitudinally varying vortex tension. The flat-kink fluctuation operator has an even translational mode and an odd shape mode of mass $\sqrt{3}/L_χ$. Reflection symmetry excludes the translational mode from the leading sourced response. We formulate the response with nonzero dressed-string boundary conditions at the longitudinal ends and derive a finite-range transverse halo. In the overlap $w\llρ\ll L_χ$, its mixed stress satisfies $2πC\,δT^{χ\,ρ}{}_l=\partial_lμ_v^{(0)}$ to leading order, where $2πC$ is the azimuthal circumference. Together with the local weak-gravity deficit relation, this supplies the leading mixed Einstein constraint of a restricted varying cone. At fixed longitudinal position the sourced halo instead decays beyond $L_χ$. Consequently, it cannot sustain that restricted cone throughout an outer overlap unless another source contributes the missing mixed stress. This obstruction is conditional on the response of the wormhole-supporting sector and is not a no-go result for general axisymmetric metrics. A finite-width calculation checks the linear-response crossover. We specify the perturbative domain and explain why a rotating extension requires an independent solution of Gauss's law. No complete backreacted wormhole solution or stability result is claimed.

gr-qc↗

arXiv2026

Rotating wormholes with a varying conical deficit: source structure and scalar mode conversion

We study a rotating traversable wormhole with an $l$-dependent conical factor, where the conical deficit is localized near the throat and vanishes in both asymptotic regions. For radial null directions we obtain \[ 8πG\,T_{μν}k^μk^ν= -2\frac{r''}{r} -\frac{α''}α -2\frac{r'α'}{rα} + \frac{N'}{N} \left( 2\frac{r'}r+\frac{α'}α \right), \] which is negative at the throat for the profiles considered here. The varying conical factor also produces the mixed Einstein-tensor component \[ G_{lθ} = -\frac{α'}α\cotθ. \] Thus the source cannot be interpreted simply as an ideal constant-tension cosmic string together with matter smooth up to the axis. For a minimally coupled massless scalar, the $m=0$ sector remains separable, while for $m\neq0$ the varying conical factor couples different angular modes. We evaluate the coupling coefficients in closed form and obtain an exact parity selection rule. In the weak-defect limit we derive the leading two-ended channel-conversion amplitude. For the $m=1$, $\ell=1\rightarrow3$ transition, the analytic result agrees with the derivative of the full coupled scattering matrix at zero defect amplitude. The numerical solution also shows the predicted $δ_s^2$ conversion scaling and is stable under enlargement of the angular basis through twelve channels.

gr-qc↗