A Theoretical Framework for Radion-Supported Gravitating Solitons: Towards a Geometric Interpretation of Confined Gauge-Field Mass

We investigate whether localized, finite-energy solutions of an Einstein-Yang-Mills-Higgs (EYMH) system coupled to a dynamically stabilized radion field admit an interpretation in which four-dimensional mass emerges from confined gauge-field flux and geometry—a phenomenon that may arise if regular, dynamically stable solutions exist. By perform- ing a dimensional reduction of a (4 + n)-dimensional bulk action over a compact internal Einstein manifold Kn, we extract a four-dimensional effective field theory (EFT) within a zero-mode Kaluza-Klein truncation where the canonical radion field dynamically couples to the Yang-Mills and Higgs kinetic sectors. Within this low-energy EFT truncation, inter- nal curvature and quantized harmonic flux generate a minimal classical effective potential Veff(ϕ) with a positive-mass minimum, ensuring radion stabilization for internal dimensions n ≥2. This structure formulates the Radion-Supported Gravitating Soliton Existence Con- jecture (RSGSEC). We derive all exponential couplings from a unified master Weyl formula, obtain the five coupled radial field equations with exact canonical dimensional uniformity, prove covariant stress-energy conservation, establish the total ADM energy functional and Derrick-Pohozaev virial identity, demonstrate analytical robustness against Derrick’s and Bekenstein’s no-go theorems, verify exact reductions to classical EYMH, ’t Hooft-Polyakov, and Bartnik-McKinnon limits, derive the second-variation linear quasinormal perturbation matrix (including the explicit closed-form radion component Ueff,ϕϕ(r)), formalize the boxed RSGSEC statement, and outline one possible functional-analysis strategy alongside numerical continuation programs required to test whether these equations admit regular, dynamically stable self-gravitating defects. 1

@article{deceuster2026_86-a-theoretical-fra,
  title = {A Theoretical Framework for Radion-Supported Gravitating Solitons: Towards a Geometric Interpretation of Confined Gauge-Field Mass},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.21313016},
  url = {https://peterdeceuster.uk/papers/86-a-theoretical-framework-for-radion-supported-gravitating-solitons},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/radionsup.pdf}
}