{
  "annotation_id": "75e5abb5-f5bf-4254-8c54-951fb86a92b2",
  "date_created": "2026-03-02T18:02:13.458000Z",
  "date_modified": "2026-03-02T18:02:13.458000Z",
  "file_hash": "af0efa97de11423d4bc9f56788988a6cc07646175b2944096dd3a1ac4641dbe2",
  "private": false,
  "record": {
    "abstract": "We calculate the bound-state energy spectrum of the Dirac Equation in a\nSchwarzschild black hole background using a minimax variational method. Our\nmethod extends that of Talman to the case of non-Hermitian interactions, such\nas a black hole. The trial function is expressed in terms of a basis set that\ntakes into account both the Hermitian limit of the interaction in the\nnon-relativistic approximation, and the general behaviour of the solutions at\nthe origin, the horizon and infinity. Using this trial function an\napproximation to the full complex energy bound-state spectrum is computed. We\nstudy the behaviour of the method as the coupling constant of the interaction\nis increased, which increases both the relativistic effects and the size of the\nnon-Hermitian part of the interaction. Finally we confirm that the method\nfollows the expected Hylleraas-Undheim behaviour.",
    "arxiv_id": "quant-ph/0503042",
    "authors": [
      "Alejandro Caceres",
      "Chris Doran"
    ],
    "categories": [
      "quant-ph",
      "gr-qc"
    ],
    "doi": "10.1103/PhysRevA.72.022103",
    "title": "Minimax determination of the energy spectrum of the Dirac equation in a   Schwarzschild background",
    "url": "https://arxiv.org/abs/quant-ph/0503042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bb02d47d-e539-4061-9a05-fca373795c9a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}