{
  "id": "0710.0171",
  "version": "v1",
  "published": "2007-09-30T20:39:57.000Z",
  "updated": "2007-09-30T20:39:57.000Z",
  "title": "A note on energy currents and decay for the wave equation on a Schwarzschild background",
  "authors": [
    "Mihalis Dafermos",
    "Igor Rodnianski"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "In recent work, we have proven uniform decay bounds for solutions of the wave equation $\\Box_g\\phi=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|\\phi|\\le Cv_+^{-1}$, which holds throughout the domain of outer communications, where $v$ is an advanced Eddington-Finkelstein coordinate, $v_+=\\max\\{v,1\\}$, and $C$ is a constant depending on a Sobolev norm of initial data. A crucial estimate in the proof required a decomposition into spherical harmonics. We here give an alternative proof of this estimate not requiring such a decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-30T20:39:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave equation",
      "energy currents",
      "schwarzschild background",
      "proven uniform decay bounds",
      "schwarzschild exterior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.0171D"
    }
  }
}