{
  "id": "2310.08611",
  "version": "v1",
  "published": "2023-10-12T00:57:19.000Z",
  "updated": "2023-10-12T00:57:19.000Z",
  "title": "Energy estimates for the Einstein-Yang-Mills fields and applications",
  "authors": [
    "Sari Ghanem"
  ],
  "comment": "55 pages. arXiv admin note: text overlap with arXiv:2310.08196, arXiv:2310.07954",
  "categories": [
    "math.AP",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "We prove exterior energy estimates for tensorial non-linear wave equations, where the background metric is a perturbation of the Minkowski space-time, and where the derivatives are the Minkowski covariant derivatives. We obtain bounds in the exterior region of the Minkowski space-time, for the weighted $L^2$ norm on each component, separately, of the covariant derivative of the tensorial solutions, and we also control a space-time integral in the exterior of the covariant tangential derivatives of the solutions. As a special application, we use here these energy estimates to prove the exterior stability of the Minkowski space-time, $\\mathbb{R}^{1+4}$, as solution to the coupled Einstein-Yang-Mills system associated to any compact Lie group $G$, in the Lorenz gauge and in wave coordinates. The bounds in the exterior for the $L^2$ norm on the covariant derivatives of each component, separately, of the tensor solution, as well as the bound on the space-time integral of the covariant tangential derivatives, are motivated by a problem that we will address in a paper that follows to prove the exterior stability of the $(1+3)$-Minkowski space-time for perturbations governed by the Einstein-Yang-Mills equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T00:57:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy estimates",
      "einstein-yang-mills fields",
      "minkowski space-time",
      "covariant tangential derivatives",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}