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
Vef f (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 Uef f,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.