{
  "id": "1501.04641",
  "version": "v1",
  "published": "2015-01-19T21:03:21.000Z",
  "updated": "2015-01-19T21:03:21.000Z",
  "title": "Decay of solutions to the Maxwell equation on the Schwarzschild background",
  "authors": [
    "Lars Andersson",
    "Thomas Bäckdahl",
    "Pieter Blue"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "gr-qc",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor $H_{ab}$ defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current $H_{ab} (\\partial_t)^b$. The tensor $H_{ab}$ vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field on the Schwarzschild exterior to the Coulomb solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-19T21:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q61",
      "83C60",
      "83C57"
    ],
    "keywords": [
      "schwarzschild background",
      "maxwell equation",
      "conserved higher order energy current",
      "integrated local energy decay estimate",
      "maxwell field"
    ],
    "publication": {
      "doi": "10.1088/0264-9381/33/8/085010",
      "journal": "Classical and Quantum Gravity",
      "year": 2016,
      "month": "Apr",
      "volume": 33,
      "number": 8,
      "pages": "085010"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1340295,
      "adsabs": "2016CQGra..33h5010A"
    }
  }
}