{
  "id": "1401.0544",
  "version": "v3",
  "published": "2014-01-02T21:04:00.000Z",
  "updated": "2014-12-19T19:30:53.000Z",
  "title": "Quasi-Normal Modes for Subtracted Rotating and Magnetised Geometries",
  "authors": [
    "M. Cvetic",
    "G. W. Gibbons",
    "Z. H. Saleem"
  ],
  "comment": "28 pages minor corrections, added references",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped, however now their oscillatory parts are shifted by the quantised wave number $k$ along the fifth circle direction.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-17T21:00:04.000Z",
      "abstract": "We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped, however now their oscillatory parts are shifted by the quantised wave number $k$ along the fifth circle direction. We also comment on the dual field theory interpretation of these results in the context of the AdS_3/CFT_2 correspondence, and note a possible phase transition in dual CFT_2 when the subtracted rotating geometry is extremal.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-19T19:30:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "04.20.Jb"
    ],
    "keywords": [
      "black hole",
      "quasi-normal modes",
      "massive five-dimensional scalar field",
      "subtracted rotating",
      "magnetised geometries"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevD.90.124046",
      "journal": "Physical Review D",
      "year": 2014,
      "month": "Dec",
      "volume": 90,
      "number": 12,
      "pages": 124046
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1275958,
      "adsabs": "2014PhRvD..90l4046C"
    }
  }
}