{
  "id": "0710.4102",
  "version": "v1",
  "published": "2007-10-22T16:50:47.000Z",
  "updated": "2007-10-22T16:50:47.000Z",
  "title": "Decay of the Maxwell field on the Schwarzschild manifold",
  "authors": [
    "P. Blue"
  ],
  "comment": "37 pages, 5 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$ for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the Regge-Wheeler tortoise coordinate is large, $r_*>\\epsilon t$, we obtain decay for the null components with rates of $|\\phi_+| \\sim |\\alpha| < C r^{-5/2}$, $|\\phi_0| \\sim |\\rho| + |\\sigma| < C r^{-2} |t-r_*|^{-1/2}$, and $|\\phi_{-1}| \\sim |\\underline{\\alpha}| < C r^{-1} |t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$, and when $t+r_*1$, all components (normalized with respect to an ingoing null basis) decay at a rate of $C \\uout^{-1}$ with $\\uout=t+r_*$ in the exterior region.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-22T16:50:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q75"
    ],
    "keywords": [
      "maxwell field",
      "schwarzschild manifold",
      "exterior region",
      "components",
      "schwarzschild black hole"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4102B"
    }
  }
}