{
  "id": "1907.08030",
  "version": "v1",
  "published": "2019-07-18T13:05:34.000Z",
  "updated": "2019-07-18T13:05:34.000Z",
  "title": "Scrambling in Hyperbolic Black Holes",
  "authors": [
    "Yongjun Ahn",
    "Viktor Jahnke",
    "Hyun-Sik Jeong",
    "Keun-Young Kim"
  ],
  "comment": "v1:20 pages, 4 figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "We study the scrambling properties of $(d+1)$-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius $\\ell$, which is dual to a $d-$dimensional conformal field theory (CFT) in hyperbolic space with temperature $T = 1/(2 \\pi \\ell)$. We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity $v_B(T)$ nicely interpolates between the Rindler-AdS result $v_B(T=\\frac{1}{2\\pi \\ell})=\\frac{1}{d-1}$ and the planar result $v_B(T \\gg \\frac{1}{\\ell})=\\sqrt{\\frac{d}{2(d-1)}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T13:05:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional conformal field theory",
      "generic hyperbolic black holes",
      "dimensional hyperbolic black holes",
      "butterfly velocity",
      "scrambling"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}