Infrared Universality: The $r^{-3}$ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915966536908800 |
|---|---|
| author | Wilson, Michael |
| author_facet | Wilson, Michael |
| contents | We identify the $r^{-3}$ curvature-decay rate as a universal geometric threshold separating compact from non-compact perturbations of Laplace-type operators on asymptotically flat manifolds. For the coupled Einstein--Maxwell system, we prove that the linearized operator $\mathcal{L}$ is essentially self-adjoint and that curvature and field strengths decaying faster than $r^{-3}$ act as relatively compact perturbations, while decay exactly at $r^{-3}$ places $0\inσ_{\mathrm{ess}}(\mathcal{L})$ through delocalized zero modes. This threshold mechanism unifies the infrared behavior of spin-1, spin-2, and mixed spin-$(1\oplus2)$ fields, linking the onset of spectral delocalization with the appearance of gravitational and electromagnetic memory. Finite-difference simulations corroborate the analytic scaling and reproduce the characteristic quadrupolar and dipolar sky maps predicted for the coupled memory fields. These results demonstrate that curvature decay at $r^{-3}$ constitutes a fundamental geometric boundary underlying infrared universality in gauge and gravitational theories, providing a spectral counterpart to the asymptotic-symmetry and soft-theorem formulations of memory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infrared Universality: The $r^{-3}$ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields Wilson, Michael General Relativity and Quantum Cosmology Mathematical Physics 83C22 (Primary) 58J50, 35P05 (Secondary) We identify the $r^{-3}$ curvature-decay rate as a universal geometric threshold separating compact from non-compact perturbations of Laplace-type operators on asymptotically flat manifolds. For the coupled Einstein--Maxwell system, we prove that the linearized operator $\mathcal{L}$ is essentially self-adjoint and that curvature and field strengths decaying faster than $r^{-3}$ act as relatively compact perturbations, while decay exactly at $r^{-3}$ places $0\inσ_{\mathrm{ess}}(\mathcal{L})$ through delocalized zero modes. This threshold mechanism unifies the infrared behavior of spin-1, spin-2, and mixed spin-$(1\oplus2)$ fields, linking the onset of spectral delocalization with the appearance of gravitational and electromagnetic memory. Finite-difference simulations corroborate the analytic scaling and reproduce the characteristic quadrupolar and dipolar sky maps predicted for the coupled memory fields. These results demonstrate that curvature decay at $r^{-3}$ constitutes a fundamental geometric boundary underlying infrared universality in gauge and gravitational theories, providing a spectral counterpart to the asymptotic-symmetry and soft-theorem formulations of memory. |
| title | Infrared Universality: The $r^{-3}$ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 83C22 (Primary) 58J50, 35P05 (Secondary) |
| url | https://arxiv.org/abs/2511.08777 |