{
  "id": "2205.12336",
  "version": "v1",
  "published": "2022-05-20T21:53:19.000Z",
  "updated": "2022-05-20T21:53:19.000Z",
  "title": "Construction of GCM hypersurfaces in perturbations of Kerr",
  "authors": [
    "Dawei Shen"
  ],
  "comment": "106 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1911.00697, arXiv:1912.12195, arXiv:2104.11857 by other authors",
  "categories": [
    "math.AP",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "This is a follow-up of \\cite{KS:Kerr1} on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in \\cite{KS:main} where decay estimates are derived in the context of nonlinear stability of Kerr family for $|a|\\ll m$. As in \\cite{KS}, the central idea of the construction of GCM hypersurfaces is to concatenate a $1$--parameter family of GCM spheres of \\cite{KS:Kerr1} by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in \\cite{KS} and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-20T21:53:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "construction",
      "perturbations",
      "full stability proof",
      "construct gcm hypersurfaces",
      "general covariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 106,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}