{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "SA5ZDFBHNZ"
    }
  ],
  "body": "\n## Summary\n\nThe Einstein–Hilbert action is the functional on Lorentzian metrics of a four-dimensional spacetime given by the integral of the [[scalar curvature|ZHX2VYQDZ3]] against the volume form.\nIts critical points are exactly the solutions of the vacuum [[Einstein field equations|3MCZ97SW6V]].\nIt casts general relativity as a variational principle, like the other field theories of physics.\n\n## Explanations\n\n### L1 human\n\nIn general relativity, gravity is the curvature of spacetime.\nThe Einstein–Hilbert action adds up the curvature over all of spacetime into one number.\nThe shapes of spacetime that make this number stationary, under small changes of the metric, are those allowed by Einstein's equations without matter.\nFor example, flat Minkowski space, the spacetime of special relativity, has no curvature at all and is such a stationary shape.\nAdding the action of matter to it gives the full Einstein equations, with matter as the source of curvature.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "83C05",
      "49S05"
    ],
    "name": "Einstein–Hilbert action",
    "same_as": {
      "wikidata": "Q239224",
      "wikipedia": "Einstein–Hilbert action"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action"
      }
    ],
    "tag": "JPE3A1SN7V"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/JPE3A1SN7V/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/JPE3A1SN7V.md",
  "msc": [
    "83C05",
    "49S05"
  ],
  "name": "Einstein–Hilbert action",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/JPE/JPE3A1SN7V.md",
  "status": null,
  "tag": "JPE3A1SN7V",
  "uri": "m2://JPE3A1SN7V",
  "url": "https://tamnd.github.io/math2/wiki/einstein-hilbert-action/",
  "writing": {
    "tag": "JPE3A1SN7V",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}