Dirac oscillator in a self-gravitating cosmic string: confinement spectra beyond the conical approximation
Abstract
The gravitational field of a physical cosmic string is regular on the axis, curved across a finite vortex core, and only asymptotically conical. We test whether the bound-state spectrum of a transverse Dirac oscillator resolves this structure beyond the ideal-cone approximation. The fermion is treated as a test field on self-consistent Einstein--Abelian-Higgs vortex backgrounds, and the radial problem is cast as a generalized Hermitian eigenvalue problem. The numerical formulation is checked against the exact Minkowski and ideal-cone spectra and by independent shooting calculations. For a reference vortex family, the finite-core correction grows from the weak-confinement regime toward the percent level. When the normalized asymptotic cone is held fixed, the spectrum still varies with the measured Higgs-core radius, and the sampled backgrounds bracket a change of sign of the ground-state correction. The bound-state spectrum therefore contains information about the resolved core profiles that is not fixed by the asymptotic cone alone.
Related
- Adiabatic confinement and number-theoretic spectra of massless Dirac fermions in twisted trilayer graphene
- Uniform approximation of spectra of linear second order differential operators via discrete sine transform based discretisation
- Real-time Dyson expansion for the nonequilibrium GW approximation: Correlated spectra and dependence on the reference propagator
- Critical Scalarization for a Self-Gravitating Bosonic Condensate
- Global and asymptotic properties of self-gravitating nonlinear sigma models
BibTeX
@misc{silva2026dirac,
title = {{Dirac oscillator in a self-gravitating cosmic string: confinement spectra beyond the conical approximation}},
author = {Edilberto O. Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20164},
eprint = {2609.20164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20164},
}
RIS
TY - UNPB
TI - Dirac oscillator in a self-gravitating cosmic string: confinement spectra beyond the conical approximation
AU - Edilberto O. Silva
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.20164
UR - https://arxiv.org/abs/2609.20164
AB - The gravitational field of a physical cosmic string is regular on the axis, curved across a finite vortex core, and only asymptotically conical. We test whether the bound-state spectrum of a transverse Dirac oscillator resolves this structure beyond the ideal-cone approximation. The fermion is treated as a test field on self-consistent Einstein--Abelian-Higgs vortex backgrounds, and the radial problem is cast as a generalized Hermitian eigenvalue problem. The numerical formulation is checked against the exact Minkowski and ideal-cone spectra and by independent shooting calculations. For a reference vortex family, the finite-core correction grows from the weak-confinement regime toward the percent level. When the normalized asymptotic cone is held fixed, the spectrum still varies with the measured Higgs-core radius, and the sampled backgrounds bracket a change of sign of the ground-state correction. The bound-state spectrum therefore contains information about the resolved core profiles that is not fixed by the asymptotic cone alone.
ER -