{"id":432,"date":"2022-01-07T14:57:24","date_gmt":"2022-01-07T05:57:24","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=432"},"modified":"2025-02-04T11:30:09","modified_gmt":"2025-02-04T02:30:09","slug":"%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%a8%e4%ba%ba%e7%94%9f%e6%9c%80%e5%a4%a7%e3%81%ae%e9%81%8e%e3%81%a1%ef%bc%9f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%a8%e4%ba%ba%e7%94%9f%e6%9c%80%e5%a4%a7%e3%81%ae%e9%81%8e%e3%81%a1%ef%bc%9f\/","title":{"rendered":"\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3068\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\uff1f"},"content":{"rendered":"

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306a\u3093\u304b\u3092\u52c9\u5f37\u3059\u308b\u3053\u3068\u81ea\u4f53\u304c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\u3060\uff0c\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u3044\u306e\u3067\u5ff5\u306e\u305f\u3081\u3002\uff08\u300c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\u300d\u3067\uff0c\u3068\u3063\u3055\u306b\u300c\u7d50\u5a5a\u300d\u3068\u304b\u300c\u53d7\u9a13\u300d\u3068\u304b\u300c\u5c31\u8077\u5148\u300d\u3068\u304b\u3092\u601d\u3044\u6d6e\u304b\u3079\u3066\u3057\u307e\u3046\u3088\u3046\u3067\u306f\uff0c\u307e\u3060\u307e\u3060\u4fee\u884c\u304c\u305f\u308a\u307e\u305b\u3093… \uff09<\/span><\/p>\n

\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb\u30fb\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/h3>\n

\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206 \\(R^{\\sigma}_{\\ \\ \\mu\\nu\\rho}\\) \u304b\u3089\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7e2e\u7d04\uff08\u6dfb\u5b57\u540c\u58eb\u3092\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04\u3067\u8db3\u3057\u3042\u3052\u308b\u3053\u3068\uff09\u3092\u3068\u3063\u3066\u4f5c\u3089\u308c\u308b \\( R_{\\mu\\rho} \\) \u3092\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u3068\u3044\u3046\u3002
\n\\begin{equation}
\nR_{\\mu\\rho} \\equiv R^{\\nu}_{\\ \\ \\mu\\nu\\rho}.
\n\\end{equation}
\n\u307e\u305f\uff0c\u3055\u3089\u306b \\(g^{\\mu\\rho}\\) \u3067\u7e2e\u7d04\u3057\u3066\u5f97\u3089\u308c\u308b
\n\\begin{equation}
\nR \\equiv g^{\\mu\\rho} R_{\\mu\\rho}
\n\\end{equation}
\n\u3092\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/strong><\/span>\u3068\u547c\u3076\u3002\u3053\u308c\u3067\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306e\u5de6\u8fba\u3092\u8868\u3059\u9053\u5177\u7acb\u3066\u304c\u63c3\u3063\u305f\u3002<\/p>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/h3>\n

\u3055\u3042\uff0c\u3044\u3088\u3044\u3088\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3067\u3042\u308b\u3002\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3068\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/strong><\/span>\u3092\u4f7f\u3046\u3068\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u308b\u3002
\n\\begin{equation}\\label{eq:ein1}
\nR_{\\mu\\nu} -\\frac{1}{2}g_{\\mu\\nu}\\, R = \\frac{8\\pi G}{c^4}
\nT_{\\mu\\nu}.
\n\\end{equation}
\n\u3053\u3053\u3067\uff0c\\(T_{\\mu\\nu}\\) \u306f\u7269\u8cea\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3067\u3042\u308a\uff0c\\(G\\) \u306f\u4e07\u6709\u5f15\u529b\u5b9a\u6570<\/strong><\/span>\uff0c\\(c\\) \u306f\u5149\u901f<\/strong><\/span>\u3067\u3042\u308b\u3002<\/p>\n

\u53f3\u8fba\u306f\uff0c\u6642\u7a7a\u306b\u5b58\u5728\u3059\u308b\u7269\u8cea\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf\u3092\u8868\u3057\uff0c\u5de6\u8fba\u306f\u305d\u306e\u7269\u8cea\u306e\u5b58\u5728\u306b\u3088\u3063\u3066\u6642\u7a7a\u304c\u66f2\u304c\u308b\uff0c\u305d\u306e\u66f2\u304c\u308a\u5177\u5408\u3092\u8868\u3059\u3002<\/p>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb<\/h4>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306e\u5de6\u8fba\u306b\u3042\u3089\u308f\u308c\u308b\uff0c\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3068\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/strong><\/span>\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u3042\u3089\u305f\u306b<\/p>\n

$$G_{\\mu\\nu} \\equiv R_{\\mu\\nu} -\\frac{1}{2}g_{\\mu\\nu}\\, R$$
\n\u3068\u5b9a\u7fa9\u3057\u3066\uff0c\\(G_{\\mu\\nu}\\) \u3092\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u3068\u547c\u3076\u3002<\/p>\n

\u5b87\u5b99\u9805\u3068\u4eba\u751f\u6700\u5927\u306e\u904e\u3061\uff1f<\/h3>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306e\u5de6\u8fba\u306f\u306a\u305c\u3053\u306e\u5f62\u306b\u66f8\u304b\u308c\u308b\u306e\u304b\u3002\u306a\u305c\u6642\u7a7a\u306e\u66f2\u304c\u308a\u5177\u5408\u3092\u76f4\u63a5\u3042\u3089\u308f\u3059\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u304f\uff0c\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3084\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/strong><\/span>\u304c\u73fe\u308c\u308b\u306e\u304b\u3002\u3053\u308c\u3089\u306e\u7591\u554f\u3078\u306e\u56de\u7b54\u306f\u672c\u7a3f\u3067\u306f\u8ff0\u3079\u308b\u4f59\u88d5\u304c\u306a\u3044\u3002\u3053\u3053\u3067\u306f\uff0c\u3053\u306e\u5f62\u306f\u7a2e\u3005\u306e\u7269\u7406\u7684\u8981\u8acb\u3092\u6e80\u305f\u3059\u3082\u306e\u306e\u3046\u3061\u3067\u6700\u3082\u5358\u7d14\u306a\u3082\u306e\u3067\u3042\u308a\uff0c\u305d\u306e\u5358\u7d14\u3055\u304c\uff0c\u63d0\u5531\u5f8c100\u5e74\u4ee5\u4e0a\u306b\u6e21\u308b\u5b9f\u8a3c\u5b9f\u9a13\u306b\u3088\u3063\u3066\u3082\u5909\u66f4\u3092\u305b\u307e\u3089\u308c\u308b\u3053\u3068\u306f\u306a\u304b\u3063\u305f\u3068\u3044\u3046\u3053\u3068\u3092\u5f37\u8abf\u3057\u3066\u304a\u304f\u306b\u3068\u3069\u3081\u308b\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n

\u3044\u3084\uff0c\u7d30\u304b\u304f\u8a00\u3046\u306a\u3089\u3070\uff0c1916\u5e74\u306b\u767a\u8868\u3055\u308c\u305f\u3053\u306e\u5f0f\u306e\u5de6\u8fba\u306f\uff0c\u305d\u306e\u7fcc\u5e74\uff0c1917\u5e74\u306b\u4ed6\u306a\u3089\u306c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u81ea\u8eab\u306b\u3088\u3063\u3066\u4e00\u65e6\u5909\u66f4\u304c\u52a0\u3048\u3089\u308c\u3066\u3044\u308b\u3002<\/p>\n

\u30cb\u30e5\u30fc\u30c8\u30f3\u540c\u69d8\uff0c\u5b87\u5b99\u306f\u6c38\u4e45\u4e0d\u5909\u3067\u3042\u308b\u3079\u3057\u3068\u8003\u3048\u3066\u3044\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\uff0c\u81ea\u8eab\u306e\u63d0\u6848\u3057\u305f\u5f0f\u304b\u3089\u306f\u6c38\u4e45\u4e0d\u5909\u306a\u5b87\u5b99\u30e2\u30c7\u30eb\u304c\u5f97\u3089\u308c\u306a\u3044\u3053\u3068\u306b\u6c17\u3065\u3044\u305f\u3002\u305d\u3053\u3067\u5f7c\u306f\uff0c\u6c38\u4e45\u4e0d\u5909\u306a\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\u3092\u5f97\u308b\u305f\u3081\uff0c\u4e07\u6709\u5f15\u529b\u3068\u53cd\u5bfe\u5411\u304d\u306e\u65a5\u529b\u3092\u4f5c\u308a\u51fa\u3059\u9805\u3092\u6b21\u5f0f\u306e\u3088\u3046\u306b\u5de6\u8fba\u306b\u4ed8\u3051\u52a0\u3048\u305f\u3002
\n\\begin{equation}
\nR_{\\mu\\nu} -\\frac{1}{2}g_{\\mu\\nu}\\, R + \\Lambda\\,g_{\\mu\\nu}
\n= \\frac{8\\pi G}{c^4}
\nT_{\\mu\\nu}.
\n\\end{equation}
\n\u3053\u3053\u3067 \\(\\Lambda\\) \u306f\u5b87\u5b99\u5b9a\u6570<\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\uff08\u6b63\u306e\uff09\u5b9a\u6570\u3067\u3042\u308a\uff0c\u5b87\u5b99\u5b9a\u6570<\/strong><\/span>\u306b\u6bd4\u4f8b\u3057\u305f\u9805 \\(\\Lambda\\,g_{\\mu\\nu}\\) \u306f\u5b87\u5b99\u9805<\/strong><\/span>\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n

\u3055\u3066\uff0c\u5b87\u5b99\u9805<\/strong><\/span>\u306e\u5c0e\u5165\u306b\u3088\u3063\u3066\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u3060\u3063\u305f\u304c\uff0c\u8a71\u306f\u3053\u3053\u3067\u7d42\u308f\u3089\u306a\u3044\u3002\u3053\u306e\u9759\u6b62\u5b87\u5b99\u30e2\u30c7\u30eb\u306f\u4e0d\u5b89\u5b9a\u3067\u3042\u308a\uff0c\u308f\u305a\u304b\u306a\u6442\u52d5\u3067\u529b\u306e\u5747\u8861\u304c\u5d29\u308c\uff0c\u5b87\u5b99\u306f\u81a8\u5f35\u307e\u305f\u306f\u53ce\u7e2e\u306b\u8ee2\u3058\u308b\u3068\u3044\u3046\u554f\u984c\u3082\u3042\u3063\u305f\u304c\uff0c\u305d\u308c\u3060\u3051\u3067\u306f\u306a\u3044\u3002<\/p>\n

\u30cf\u30c3\u30d6\u30eb\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u306e\u6cd5\u5247\uff1a\u81a8\u5f35\u5b87\u5b99\u306e\u767a\u898b<\/h3>\n

1929\u5e74\uff0c\u305d\u306e\u5f8c\u306e\u5b87\u5b99\u8ad6\u7814\u7a76\u3092\u6c7a\u5b9a\u3065\u3051\u308b\u7814\u7a76\u7d50\u679c\u304c\u767a\u8868\u3055\u308c\u305f\u3002\u30cf\u30c3\u30d6\u30eb\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u306e\u6cd5\u5247<\/strong><\/span>\uff08\u73fe\u5728\u3067\u306f\u30cf\u30c3\u30d6\u30eb\u306e\u6cd5\u5247<\/strong><\/span>\u3067\u306f\u306a\u304f\u30cf\u30c3\u30d6\u30eb\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u306e\u6cd5\u5247<\/strong><\/span>\u3068\u547c\u3076\u306e\u304c\u304a\u4f5c\u6cd5\uff09\u3067\u3042\u308b\u3002<\/p>\n

\u30cf\u30c3\u30d6\u30eb\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u306e\u6cd5\u5247<\/strong><\/span>\u3068\u306f\uff0c\u76f4\u63a5\u7684\u306b\u306f\u9060\u65b9\u306e\u9280\u6cb3\u306e\u5f8c\u9000\u901f\u5ea6\uff08\u3068\u3044\u3046\u89b3\u6e2c\u91cf\uff09\u304c\u305d\u306e\u8ddd\u96e2\uff08\u3068\u3044\u3046\u89b3\u6e2c\u91cf\uff09\u306b\u6bd4\u4f8b\u3059\u308b\u3068\u3044\u3046\u6cd5\u5247\uff0c\u3064\u307e\u308a2\u3064\u306e\u89b3\u6e2c\u91cf\u9593\u306e\u6bd4\u4f8b\u95a2\u4fc2\u3092\u8868\u3057\u3066\u3044\u308b\u3002<\/p>\n

\u3053\u306e\u95a2\u4fc2\u306b\uff0c\u5b87\u5b99\u306f\u5927\u57df\u7684\u30fb\u5e73\u5747\u7684\u306b\u307f\u308c\u3070\u4e00\u69d8\u7b49\u65b9\u3067\u3042\u308b\u3068\u3044\u3046\uff08\u4f5c\u696d\u4eee\u8aac\u3068\u3057\u3066\u306e\uff09\u300c\u5b87\u5b99\u539f\u7406<\/strong><\/span>\u300d\u306e\u4eee\u5b9a\u3092\u4ed8\u3051\u52a0\u3048\u308b\u3068\uff0c\u30cf\u30c3\u30d6\u30eb\u30fb\u30eb\u30e1\u30fc\u30c8\u30eb\u306e\u6cd5\u5247<\/strong><\/span>\u304c\u8868\u3057\u3066\u3044\u308b\u306e\u306f\u500b\u3005\u306e\u9280\u6cb3\u306e\u904b\u52d5\u3067\u306f\u306a\u304f\uff0c\u9280\u6cb3\u304c\u5165\u3063\u3066\u3044\u308b\u5165\u308c\u7269\u3067\u3042\u308b\u5b87\u5b99\u7a7a\u9593\u305d\u306e\u3082\u306e\u306e\u81a8\u5f35\u306a\u306e\u3060\uff0c\u3068\u3044\u3046\u7d50\u8ad6\u304c\u5c0e\u304b\u308c\u308b\u3002<\/p>\n

\u5b87\u5b99\u306f\u9759\u6b62\u306a\u3069\u3057\u3066\u3044\u306a\u3044\u3002\u300c\u5b87\u5b99\u306f\u81a8\u5f35\u3057\u3066\u3044\u308b<\/strong><\/span>\u300d\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u4e8b\u5b9f\u3092\u805e\u3044\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\uff0c\u5b87\u5b99\u5b9a\u6570<\/strong><\/span>\u3092\u5c0e\u5165\u3057\u305f\u3053\u3068\u306f\u300c\u4eba\u751f\u6700\u5927\u306e\u904e\u3061<\/strong><\/span>\u300d\u3060\u3063\u305f\u3068\u3057\u3066\u53d6\u308a\u4e0b\u3052\u3066\u3057\u307e\u3046\u3002<\/p>\n

\u679c\u305f\u3057\u3066\u672c\u5f53\u306b\u4eba\u751f\u6700\u5927\u306e\u904e\u3061<\/strong><\/span>\u3060\u3063\u305f\u306e\u3060\u308d\u3046\u304b\uff1f<\/p>\n

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