{
  "annotation_id": "f75def5d-4109-4a05-bdff-23fb042386ba",
  "date_created": "2026-02-17T05:53:15.228000Z",
  "date_modified": "2026-02-17T05:53:15.228000Z",
  "file_hash": "02fc85ffb4476f6a510c94f5e1fe33dc2ef56656791f0328143a7910dac0450e",
  "private": false,
  "record": {
    "abstract": "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.",
    "arxiv_id": "2601.08501",
    "authors": [
      "Emel Altas",
      "Bayram Tekin"
    ],
    "categories": [
      "gr-qc",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections",
    "url": "https://arxiv.org/abs/2601.08501",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c546d955-0036-45cf-b382-b10b8c941c49",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}