Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915752191197184 |
|---|---|
| author | Altas, Emel Tekin, Bayram |
| author_facet | Altas, Emel Tekin, Bayram |
| contents | Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor obeys a wave equation of the schematic form \[ \Box Riem=\mathcal{Q}(Riem,Riem), \] where $\mathcal{Q}(Riem,Riem)$ denotes the terms quadratic in the curvature arising from the Bianchi identities. In this work, we generalize this curvature wave equation to spacetimes endowed with a generic affine connection possessing torsion and nonmetricity. Working within the metric-affine framework, we derive the corresponding wave equation for the Riemann tensor and analyze its structure in several geometrically and physically distinguished settings, including Einstein spaces, teleparallel gravity, and Einstein-Cartan theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections Altas, Emel Tekin, Bayram General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor obeys a wave equation of the schematic form \[ \Box Riem=\mathcal{Q}(Riem,Riem), \] where $\mathcal{Q}(Riem,Riem)$ denotes the terms quadratic in the curvature arising from the Bianchi identities. In this work, we generalize this curvature wave equation to spacetimes endowed with a generic affine connection possessing torsion and nonmetricity. Working within the metric-affine framework, we derive the corresponding wave equation for the Riemann tensor and analyze its structure in several geometrically and physically distinguished settings, including Einstein spaces, teleparallel gravity, and Einstein-Cartan theory. |
| title | Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2601.08501 |