{
  "id": "2106.01966",
  "version": "v1",
  "published": "2021-06-03T16:12:59.000Z",
  "updated": "2021-06-03T16:12:59.000Z",
  "title": "Quantization of Gravity in the Black Hole Background",
  "authors": [
    "Renata Kallosh",
    "Adel A. Rahman"
  ],
  "comment": "29 p",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number $l \\geq 2$, while for low multipole modes with $l$ $=$ $0$ or $1$ -- for which Regge-Wheeler gauge is inapplicable -- we propose a set of gauge fixing conditions which are 2D background covariant and perturbatively well-defined. We find that the corresponding Faddeev-Popov ghosts are non-propagating for the $l\\geq2$ modes, but are in general nontrivial for the low multipole modes with $l = 0,1$. However, in Schwarzschild coordinates, all time derivatives acting on the ghosts drop from the action and the low multipole ghosts have instantaneous propagators. Up to possible subtleties related to quantizing gravity in a space with a horizon, Faddeev's theorem suggests the possibility of an underlying canonical (Hamiltonian) quantization with a ghost-free Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-03T16:12:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "black hole background",
      "quantization",
      "low multipole modes",
      "angular momentum quantum number",
      "low multipole ghosts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}