{"id":491,"date":"2023-01-03T10:46:48","date_gmt":"2023-01-03T01:46:48","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=491"},"modified":"2025-08-09T20:27:44","modified_gmt":"2025-08-09T11:27:44","slug":"post-491","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=491","title":{"rendered":"\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f"},"content":{"rendered":"\n

\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001\u8cea\u91cf\u3068\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f\u306e\u3067\u3001\u91cd\u529b\u306e\u6e90\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6\u3067\u3042\u308b\u3068\u8a00\u3044\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002
\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6\u306f\u5358\u72ec\u3067\u306f\u30c6\u30f3\u30bd\u30eb\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u904b\u52d5\u91cf\u5bc6\u5ea6\u3068\u5408\u308f\u305b\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb$T_{\\mu\\nu}$\u3092\u7528\u3044\u3066\u65b9\u7a0b\u5f0f\u3092\u69cb\u6210\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001\u65b9\u7a0b\u5f0f\u3092\u4eee\u306b\u3001$\\kappa$\u3092\u4fc2\u6570\u3068\u3057\u3066\u3001$X^{\\mu\\nu}=\\kappa T^{\\mu\\nu}$\u3068\u66f8\u3044\u3066\u304a\u304f\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u306f$\\partial_{\\mu}T^{\\mu\\nu}=0$\u3068\u3044\u3046\u95a2\u4fc2(\u30a8\u30cd\u30eb\u30ae\u30fc\u304a\u3088\u3073\u904b\u52d5\u91cf\u306e\u4fdd\u5b58)\u3092\u6e80\u305f\u3057\u307e\u3059\u3002
\u30c6\u30f3\u30bd\u30eb\u3092\u305f\u3060\u5fae\u5206\u3057\u305f\u3082\u306e\u306f\u30c6\u30f3\u30bd\u30eb\u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\u3001\u5171\u5909\u5fae\u5206\u3092\u7528\u3044\u3066\u3001$\\nabla_{\\mu}T^{\\mu\\nu}=0$\u3068\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u305d\u3046\u3059\u308b\u3068\u3001\u5de6\u8fba\u306e$X^{\\mu\\nu}$\u3092\u5171\u5909\u5fae\u5206\u3057\u305f\u3082\u306e\u306b\u3064\u3044\u3066\u3082$\\nabla_{\\mu}X^{\\mu\\nu}=0$\u304c\u6210\u308a\u7acb\u3064\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002
\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059$X^{\\mu\\nu}$\u306e\u5019\u88dc\u3068\u3057\u3066\u3001\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb$G^{\\mu\\nu}$\u304c\u3042\u308a\u307e\u3059\u3002
\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

$$\nG^{\\mu\\nu}=\\kappa T^{\\mu\\nu}\n$$<\/p>\n\n\n\n

\u3068\u3057\u3066\u304a\u3051\u3070\u3088\u3055\u305d\u3046\u3067\u3059\u3002
\u3053\u306e\u5f0f\u3092\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong>(Einstein’s equations)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n

\u6dfb\u5b57\u306f\u4e0b\u4ed8\u304d\u306b\u3057\u3066\u3042\u308b\u3053\u3068\u304c\u591a\u3044\u306e\u3067\u3001\u3053\u3053\u3067\u3082\u4e0b\u4ed8\u304d\u306b\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

$$
G_{\\mu\\nu}=\\kappa T_{\\mu\\nu}
$$<\/p>\n\n\n\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u5de6\u8fba\u306b\u3064\u3044\u3066\u3001\u5225\u306b\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb\u3067\u306a\u304f\u3066\u3082\u3044\u3044\u306e\u3067\u306f\u3001\u3068\u601d\u308f\u308c\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002
\u3057\u304b\u3057\u3001\u6b21\u306b\u793a\u3059\u30e9\u30d6\u30ed\u30c3\u30af\u306e\u5b9a\u7406\u3088\u308a\u3001\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb\u3092\u7528\u3044\u308b\u306e\u304c\u59a5\u5f53\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\n\n\n\n

\u30e9\u30d6\u30ed\u30c3\u30af\u306e\u5b9a\u7406<\/strong>(Lovelock’s theorem)<\/p>\n\n\n\n

2\u968e\u306e\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb$H_{\\mu\\nu}$\u306e\u3046\u3061\u3001<\/p>\n\n\n\n

    \n
  1. \u8a08\u91cf\u306e2\u968e\u5fae\u5206\u307e\u3067\u3067\u8868\u3055\u308c\u308b: $H_{\\mu\\nu}=H_{\\mu\\nu}(g_{\\alpha\\beta},\\partial_{\\gamma}g_{\\alpha\\beta},\\partial_{\\gamma}\\partial_{\\delta}g_{\\alpha\\beta})$<\/li>\n\n\n\n
  2. \u767a\u6563\u304c0\u306b\u306a\u308b: $\\nabla^{\\alpha}H_{\\alpha\\beta}=0$<\/li>\n\n\n\n
  3. \u6642\u7a7a\u304c4\u6b21\u5143\u3067\u3042\u308b\u304b\u3001\u3082\u3057\u304f\u306f$H_{\\mu\\nu}$\u304c$\\partial_{\\alpha}\\partial_{\\beta}g_{\\mu\\nu}$\u306b\u3064\u3044\u3066\u7dda\u5f62\u3067\u3042\u308b<\/li>\n<\/ol>\n\n\n\n

    \u306e\u3059\u3079\u3066\u3092\u6e80\u305f\u3059\u3082\u306e\u306f\u3001$H_{\\mu\\nu}=C_1G_{\\mu\\nu}+C_2g_{\\mu\\nu}$\u306b\u9650\u3089\u308c\u308b($C_1,C_2$\u306f\u5b9a\u6570)<\/p>\n\n\n\n

    \n\n\n\n

    \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u306f2\u968e\u306e\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb\u306a\u306e\u3067\u3001\u5de6\u8fba\u30822\u968e\u306e\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002
    \u305d\u306e\u3088\u3046\u306a\u30c6\u30f3\u30bd\u30eb\u306e\u3046\u3061\u3001\u9069\u5207\u306a\u3082\u306e\u306f$H_{\\mu\\nu}=C_1G_{\\mu\\nu}+C_2g_{\\mu\\nu}$\u3067\u8868\u3055\u308c\u308b\u30c6\u30f3\u30bd\u30eb\u306b\u9650\u3089\u308c\u308b\u3001\u3068\u3044\u3046\u5185\u5bb9\u3067\u3059\u3002
    \u3057\u305f\u304c\u3063\u3066\u3001\u5de6\u8fba\u306b\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb$G_{\\mu\\nu}$\u3092\u7528\u3044\u308b\u306e\u304c\u59a5\u5f53\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    $$ G_{\\mu\\nu}+\\lambda g_{\\mu\\nu}=\\kappa T_{\\mu\\nu} $$<\/p>\n\n\n\n

    \u3053\u3053\u3067\u65b0\u3057\u304f\u8ffd\u52a0\u3055\u308c\u305f$\\lambda g_{\\mu\\nu}$\u306e\u9805\u3092\u5b87\u5b99\u9805<\/strong>(cosmological term)\u3001$\\lambda$\u3092\u5b87\u5b99\u5b9a\u6570<\/strong>(cosmological constant)\u3068\u547c\u3073\u307e\u3059\u3002
    \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\u5f53\u521d\u3001\u5b9a\u5e38\u306a\u5b87\u5b99\u3092\u60f3\u5b9a\u3057\u3066\u304a\u308a\u3001\u305d\u308c\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306b\u5b87\u5b99\u9805\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3057\u305f\u3002
    \u5f8c\u306b\u3001\u5b87\u5b99\u306f\u5b9a\u5e38\u3067\u306f\u306a\u304f\u81a8\u5f35\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u3001\u5b87\u5b99\u9805\u306f\u53d6\u308a\u4e0b\u3052\u3089\u308c\u307e\u3057\u305f\u3002
    \u3057\u304b\u3057\u3001\u8fd1\u5e74\u306e\u5b87\u5b99\u8ad6\u3067\u306f\u3001\u3084\u306f\u308a\u5b87\u5b99\u9805\u304c\u5fc5\u8981\u3060\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002<\/p>\n\n\n\n

    \u5b87\u5b99\u9805\u306b\u3064\u3044\u3066\u306f\u6c17\u304c\u5411\u3044\u305f\u3089\u8abf\u67fb\u3059\u308b\u3068\u3057\u3066\u3001\u3053\u3053\u304b\u3089\u3057\u3070\u3089\u304f\u306f\u5b87\u5b99\u9805\u306a\u3057\u306e\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u8003\u3048\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001\u8cea\u91cf\u3068\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f\u306e\u3067\u3001\u91cd\u529b\u306e\u6e90\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6\u3067\u3042\u308b\u3068\u8a00\u3044\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6\u306f\u5358\u72ec\u3067\u306f\u30c6\u30f3\u30bd\u30eb\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u904b\u52d5\u91cf\u5bc6\u5ea6\u3068\u5408\u308f\u305b\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-491","post","type-post","status-publish","format-standard","hentry","category-9","category-10"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/491","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=491"}],"version-history":[{"count":5,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/491\/revisions"}],"predecessor-version":[{"id":1498,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/491\/revisions\/1498"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=491"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}