Radion-Supported Gravitating Solitons in Flux-Stabilized Kaluza–Klein Compactifications

We provide a classical effective-field-theory formulation for localized finite-energy con- figurations possessing an effective gravitational mass scale via warped compactification of an Einstein–Yang–Mills–Higgs system. Working within the lowest-mode Kaluza–Klein truncation—valid provided gradients and defect energies remain below the first KK exci- tation scale—we define a localized radion core as a region in which the radion, gauge, and Higgs profiles depart from their asymptotic compactification values, creating a finite-energy soliton configuration. Tracking the logarithmic radion field σ = ln Ψ through a Weyl confor- mal transformation, we derive its Einstein-frame kinetic term and identify the canonically normalized field. By explicitly integrating a topologically normalized harmonic flux over the reference metric, we remove scaling ambiguities and derive the Einstein-frame effective potential within the lowest-mode truncation. After detailing the radion-gauge derivative mixing and the resulting Effective Field Theory (EFT) expansion, we formulate the fully coupled nonlinear boundary-value problem for a gravitating monopole sector. The explicit existence of these radion-supported solitons remains to be established via numerical investi- gation of the resulting system of five coupled nonlinear radial equations for the gauge, Higgs, radion, and metric functions. 1 Dimensional Reduction and Weyl Rescaling We consider a (4 + n)-dimensional action governed by gravity and a gauge sector. We assume the factorizable metric ansatz ds2 = gµνdxµdxν + e2σ(x)γabdyadyb. Following standard Kaluza- Klein conventions, the higher-dimensional Ricci scalar decomposes as R(4+n) = R(4)+e−2σRK− 2n□(4)σ−n(n+1)(∂σ)2. Integrating over the internal manifold Kn with volume VK, the Jordan- frame gravitational sector is: S4 ⊃ Z d4x√−gM2 Pl 2 enσ h R(4) + e−2σRK + n(n −1)(∂σ)2i (1) 1

@article{deceuster2026_88-radion-supported-,
  title = {Radion-Supported Gravitating Solitons in Flux-Stabilized Kaluza–Klein Compactifications},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.21309825},
  url = {https://peterdeceuster.uk/papers/88-radion-supported-gravitating-solitons-in-flux-stabilized-kaluzaklein},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/sol.pdf}
}