Bewaard in:
| Hoofdauteur: | |
|---|---|
| Formaat: | Recurso digital |
| Taal: | |
| Gepubliceerd in: |
Zenodo
2026
|
| Onderwerpen: | |
| Online toegang: | https://doi.org/10.5281/zenodo.19637085 |
| Tags: |
Voeg label toe
Geen labels, Wees de eerste die dit record labelt!
|
Inhoudsopgave:
- <p>This work (S-4) unifies the time-scale structure developed in S-2 and the spatial scale structure developed in S-3, and derives the Shadow Quantum Gravity Equation. Under three minimal conditions—differentiability, local invertibility, and consistency—the spacetime scale transformation is uniquely generated by</p> <p> K = K_t + K_x = k_t * partial_t + k_x * Delta,</p> <p>which yields a closed spacetime scale flow for any field Phi_ell:</p> <p> d/dell Phi_ell = k_t * partial_t Phi_ell + k_x * Delta Phi_ell.</p> <p>The time direction produces a decay structure, while the spatial direction produces a coarse-graining structure, and both arise from a single unified scale principle.</p> <p>In the Kerr background, the spatial Laplacian is replaced by Delta_Kerr, leading to a scale-dependent radial equation that defines the Shadow Quantum Gravity Equation. This formulation clarifies the geometric origin of the QNM decay structure D(L), and naturally produces the scale-dependent deformation of the Kerr potential and the resulting QNM frequency shifts.</p> <p>This paper completes the mathematical foundation of spacetime scale hierarchies and establishes the framework of shadow quantum gravity. The S-4 equation provides a unified theoretical basis for scale-dependent QNM analysis and opens the path toward the source-side theory (S-5).</p>