{
  "annotation_id": "8b798571-78e4-4fe1-8535-a9b2cd8bde64",
  "date_created": "2026-03-02T18:01:17.372000Z",
  "date_modified": "2026-03-02T18:01:17.372000Z",
  "file_hash": "1dbdf1b391dfe668960556568d71c9170ccb801ef922ff2f20baab4a50cafe92",
  "private": false,
  "record": {
    "abstract": "This article reports on a student summer project performed in 2006 at the\nUniversity of Frankfurt. It is addressed to undergraduate students familiar\nwith the basic principles of relativistic quantum mechanics and general\nrelativity. The aim of the project was to study the Dirac equation in curved\nspace time. To obtain the general relativistic Dirac equation we use the\nformulation of gravity as a gauge theory in the first part. After these general\nconsiderations we restrict the further discussion to the special case of the\nSchwarzschild metric. This setting corresponds to the hydrogen atom, with the\nelectromagnetic field replaced by gravity. Although there is a singularity at\nthe event horizon it turns out that a regular solution of the time independent\nDirac equation exists. Finally the Dirac equation is solved numerically using\nsuitable boundary conditions.",
    "arxiv_id": "physics/0703064",
    "authors": [
      "Martin Kober",
      "Benjamin Koch",
      "Marcus Bleicher"
    ],
    "categories": [
      "physics.ed-ph",
      "physics.pop-ph"
    ],
    "doi": "10.1088/0143-0807/28/3/007",
    "journal_ref": "Eur.J.Phys.28:465-478,2007",
    "title": "The gravitational analogue to the hydrogen atom (A summer study at the   borders of quantum mechanics and general relativity)",
    "url": "https://arxiv.org/abs/physics/0703064"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9a6ee4aa-0d5f-4191-9856-efe4d030cc77",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}