{
  "id": "2008.11429",
  "version": "v1",
  "published": "2020-08-26T07:52:34.000Z",
  "updated": "2020-08-26T07:52:34.000Z",
  "title": "Sharp decay estimates for massless Dirac fields on a Schwarzschild background",
  "authors": [
    "Siyuan Ma",
    "Lin Zhang"
  ],
  "comment": "65 pages, 6 figures, 1 table",
  "categories": [
    "math.AP",
    "gr-qc",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove a uniform bound estimate for a positive definite energy and an integrated local energy decay estimate for the spin $s=\\pm \\frac{1}{2}$ components of the Dirac field. Based on these estimates and depending on the asymptotics of the initial data, we further show these components have pointwise decay $c_1v^{-3/2-s}\\tau^{-3/2+s}$ or $c_2v^{-3/2-s}\\tau^{-5/2+s}$ as both an upper and a lower bound, with constants $c_1$ and $c_2$ explicitly expressed in terms of the initial data. This establishes the validity of the conjectured Price's law for massless Dirac fields outside a Schwarzschild black hole.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-26T07:52:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q75",
      "58K55",
      "35L45",
      "58J45",
      "83C30"
    ],
    "keywords": [
      "massless dirac fields",
      "sharp decay estimates",
      "schwarzschild background",
      "initial data",
      "integrated local energy decay estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}