{
  "id": "2212.12332",
  "version": "v1",
  "published": "2022-12-23T13:39:20.000Z",
  "updated": "2022-12-23T13:39:20.000Z",
  "title": "JT gravity and near-extremal thermodynamics for Kerr black holes in $AdS_{4,5}$ for rotating perturbations",
  "authors": [
    "Rohan R. Poojary"
  ],
  "categories": [
    "hep-th"
  ],
  "abstract": "We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum $\\delta J $ and excess mass $\\delta M$ is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr $AdS_4$ we hold $\\delta J-\\mathcal{L}\\,\\delta M=0 $ while for Myers-Perry(MP) type Kerr black hole in $AdS_5$ we hold $\\delta J_{\\varphi_{1,2}}\\hspace{-0.2cm}-\\mathcal{L}_{\\varphi_{1,2}}\\,\\delta M=0$. We show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture the thermodynamics of the higher dimensional black holes at small near extremal temperatures $T_H$. We show this by generalizing the near horizon limits found in literature by parameters $\\mathcal{L}$ and $\\mathcal{L}_{\\varphi_{1,2}}$ for the two geometries. The resulting JT theory captures the near extremal thermodynamics of such geometries provided we identify the temperature $T^{(2)}_H$ of the near horizon $AdS_2$ geometry to be $T^{(2)}_H=T_H/(1-\\mu\\,\\mathcal{L})$ for 4d Kerr and $T^{(2)}_H=T_H/(1-\\mu\\,(\\mathcal{L}_{\\varphi_1}+\\mathcal{L}_{\\varphi_2}))$ for 5d Kerr where $\\mu$ is their chemical potential, with $\\mu\\,\\mathcal{L}<1$ and $\\mu\\,(\\mathcal{L}_{\\varphi_1}+\\mathcal{L}_{\\varphi_2})<1$ respectively. We also argue that such a theory embeds itself non-trivially in the higher dimensional theory dual to the Kerr geometries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-23T13:39:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jt gravity",
      "near-extremal thermodynamics",
      "rotating perturbations",
      "higher dimensional theory dual",
      "higher dimensional black holes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}