{"id":440,"date":"2022-01-07T15:16:36","date_gmt":"2022-01-07T06:16:36","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=440"},"modified":"2023-05-17T16:24:12","modified_gmt":"2023-05-17T07:24:12","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab%e3%81%ae%e6%80%a7%e8%b3%aa","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\/%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab%e3%81%ae%e6%80%a7%e8%b3%aa\/","title":{"rendered":"\u88dc\u8db3\uff1a\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u6027\u8cea"},"content":{"rendered":"

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206 \\(G^{\\mu}_{\\ \\\u00a0 \\gamma}\\) \u3092\u4ee5\u4e0b\u306e\u5b9a\u7fa9\u3059\u308b\u3068\uff0c
\n$$G^{\\mu}_{\\ \\\u00a0 \\gamma} \\equiv R^{\\mu}_{\\ \\\u00a0 \\gamma} – \\frac{1}{2} \\delta^{\\mu}_{\\ \\\u00a0 \\gamma} R$$
\n\u7e2e\u7d04\u3055\u308c\u305f\u30d3\u30a2\u30f3\u30ad\u6052\u7b49\u5f0f<\/strong><\/span>\u304b\u3089\uff0c(1,1)-\u578b\u306e\u30c6\u30f3\u30bd\u30eb\uff0c\u3064\u307e\u308a\u4e0a\u6dfb\u5b571\u3064\u4e0b\u6dfb\u5b571\u3064\u306e\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306e\u5171\u5909\u5fae\u5206<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7c21\u6f54\u306b\u66f8\u3051\u308b\u3053\u3068\u3092\u793a\u3059\u3002\uff08\u3053\u3053\u3067\u306f\u6975\u529b\u300c\u5171\u5909\u5fae\u5206<\/strong><\/span>\u300d\u3092\u4f7f\u3063\u3066\u3053\u306a\u304b\u3063\u305f\u306e\u3067\uff0c\u5b9a\u7fa9\u306b\u3064\u3044\u3066\u306f\u5225\u9014\u3002\uff09
\n$$G^{\\mu}_{\\ \\\u00a0 \\gamma; \\mu} = 0$$<\/p>\n

\n

\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206<\/h3>\n

\u30ea\u30fc\u30de\u30f3\u30ec\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206 \\( R^{\\mu}_{\\ \\ \\ \\nu\\alpha\\beta}\\)\u306f\uff0c\u4ee5\u4e0b\u306e\u5f0f\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u305f\u3002
\n$$\\boldsymbol{e}_{\\nu, \\beta\\alpha} – \\boldsymbol{e}_{\\nu, \\alpha\\beta} \\equiv R^{\\mu}_{\\ \\ \\ \\nu\\alpha\\beta}\\,\\boldsymbol{e}_{\\mu}$$<\/p>\n

\u3053\u3053\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u4ea4\u63db\u5b50\u3092\u5b9a\u7fa9\u3059\u308b\u3068\uff0c
\n$$ [\\partial_{\\alpha}, \\partial_{\\beta}] \\equiv \\frac{\\partial}{\\partial x^{\\alpha}} \\frac{\\partial}{\\partial x^{\\beta}} – \\frac{\\partial}{\\partial x^{\\beta}}\\frac{\\partial}{\\partial x^{\\alpha}}$$
\n$$[\\partial_{\\alpha}, \\partial_{\\beta}] \\boldsymbol{e}_{\\nu} = R^{\\mu}_{\\ \\ \\ \\nu\\alpha\\beta}\\,\\boldsymbol{e}_{\\mu}$$ \u3068\u66f8\u3051\u308b\u3002<\/p>\n

\u3053\u306e\u4ea4\u63db\u5b50\u306f\uff0c\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306a\u3069\u306e\u95a2\u6570\u306b\u4f5c\u7528\u3059\u308b\u3068\uff08\u504f\u5fae\u5206\u306f\u4ea4\u63db\u53ef\u80fd\u3067\u3042\u308b\u304b\u3089\uff09\u305f\u3060\u3061\u306b\u30bc\u30ed\u306b\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u57fa\u5e95\uff08\u57fa\u672c\u30d9\u30af\u30c8\u30eb\uff09\u3078\u306e\u4f5c\u7528\u3060\u3051\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u3002<\/p>\n

\u30e4\u30b3\u30d3\u6052\u7b49\u5f0f<\/h3>\n

\u30e4\u30b3\u30d3\u6052\u7b49\u5f0f<\/strong><\/span><\/span>\u3068\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f0f\u3067\u3042\u308b\u3002\u3044\u304b\u306a\u308b\u5bfe\u8c61\u306b\u4f5c\u7528\u3059\u308b\u304b\u306b\u95a2\u4fc2\u306a\u304f\uff0c\u6f14\u7b97\u5b50\u306e\u307e\u307e\u3067\u6052\u7b49\u7684\u306b\u6210\u308a\u7acb\u3064\u3002
\n$$\\bigl[\\partial_{\\gamma}, [\\partial_{\\alpha}, \\partial_{\\beta}]\\bigr] +
\n\\bigl[\\partial_{\\alpha}, [\\partial_{\\beta}, \\partial_{\\gamma}]\\bigr]+
\n\\bigl[\\partial_{\\beta}, [\\partial_{\\gamma}, \\partial_{\\alpha}]\\bigr] =0$$ \u3053\u308c\u306f\u76f4\u63a5\u66f8\u304d\u51fa\u3057\u3066\u8a3c\u660e\u3067\u304d\u308b\u3002\u540c\u3058\u8272\u306e\u9805\u304c\u30ad\u30e3\u30f3\u30bb\u30eb\u3057\u3042\u3063\u3066\u30bc\u30ed\u306b\u306a\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n\\bigl[\\partial_{\\gamma}, [\\partial_{\\alpha}, \\partial_{\\beta}]\\bigr] &=&
\n\\partial_{\\gamma}(\\partial_{\\alpha}\\partial_{\\beta}-\\partial_{\\beta}\\partial_{\\alpha}) – (\\partial_{\\alpha}\\partial_{\\beta}-\\partial_{\\beta}\\partial_{\\alpha})\\partial_{\\gamma} \\\\
\n&=&\\color{blue}{\\partial_{\\gamma}\\partial_{\\alpha}\\partial_{\\beta} } \\color{purple}{- \\partial_{\\gamma}\\partial_{\\beta}\\partial_{\\alpha} } \\color{green}{-
\n\\partial_{\\alpha}\\partial_{\\beta}\\partial_{\\gamma}} \\color{cyan}{+
\n\\partial_{\\beta}\\partial_{\\alpha}\\partial_{\\gamma}} \\\\
\n\\bigl[\\partial_{\\alpha}, [\\partial_{\\beta}, \\partial_{\\gamma}]\\bigr]&=&
\n\\color{green}{\\partial_{\\alpha}\\partial_{\\beta}\\partial_{\\gamma} } \\color{red}{-
\n\\partial_{\\alpha}\\partial_{\\gamma}\\partial_{\\beta} }
\n\\color{black}{-\\partial_{\\beta}\\partial_{\\gamma}\\partial_{\\alpha}} \\color{purple}{+
\n\\partial_{\\gamma}\\partial_{\\beta}\\partial_{\\alpha}} \\\\
\n\\bigl[\\partial_{\\beta}, [\\partial_{\\gamma}, \\partial_{\\alpha}]\\bigr] &=&
\n\\partial_{\\beta}\\partial_{\\gamma}\\partial_{\\alpha} \\color{cyan}{-
\n\\partial_{\\beta}\\partial_{\\alpha}\\partial_{\\gamma}} \\color{blue}{-
\n\\partial_{\\gamma}\\partial_{\\alpha}\\partial_{\\beta}} \\color{red}{+
\n\\partial_{\\alpha}\\partial_{\\gamma}\\partial_{\\beta}}
\n\\end{eqnarray}<\/p>\n

\u30e4\u30b3\u30d3\u6052\u7b49\u5f0f\u304b\u3089\u30d3\u30a2\u30f3\u30ad\u6052\u7b49\u5f0f\u3078<\/h3>\n

\\begin{eqnarray}
\n\\bigl[\\partial_{\\gamma}, [\\partial_{\\alpha}, \\partial_{\\beta}]\\bigr] \\boldsymbol{e}_{\\nu} &=&
\n\\left( [\\partial_{\\alpha}, \\partial_{\\beta}]\\boldsymbol{e}_{\\nu}\\right)_{,\\gamma} – [\\partial_{\\alpha}, \\partial_{\\beta}] \\boldsymbol{e}_{\\nu, \\gamma}\u00a0 \\\\
\n&=& \\left(R^{\\mu}_{\\ \\ \\ \\nu\\alpha\\beta}\\boldsymbol{e}_{\\mu}\\right)_{,\\gamma} – [\\partial_{\\alpha}, \\partial_{\\beta}]\\left( \\Gamma^{\\lambda}_{\\ \\ \\nu\\gamma} \\boldsymbol{e}_{\\lambda}\\right)\\\\
\n&=& R^{\\mu}_{\\ \\ \\\u00a0 \\nu\\alpha\\beta, \\gamma}\\boldsymbol{e}_{\\mu} + R^{\\mu}_{\\ \\ \\\u00a0 \\nu\\alpha\\beta}\\boldsymbol{e}_{\\mu, \\gamma} – \\Gamma^{\\lambda}_{\\ \\ \\nu\\gamma} [\\partial_{\\alpha}, \\partial_{\\beta}]\\boldsymbol{e}_{\\lambda} \\\\
\n&=& \\left( R^{\\mu}_{\\ \\ \\\u00a0 \\nu\\alpha\\beta, \\gamma} + R^{\\lambda}_{\\ \\ \\\u00a0 \\nu\\alpha\\beta} \\Gamma^{\\mu}_{\\ \\ \\lambda\\gamma} -R^{\\mu}_{\\ \\ \\\u00a0 \\lambda\\alpha\\beta} \\Gamma^{\\lambda}_{\\ \\ \\nu\\gamma} \\right) \\boldsymbol{e}_{\\mu}
\n\\end{eqnarray}<\/p>\n

\u3057\u305f\u304c\u3063\u3066\uff0c<\/p>\n

$$\\Bigl(\\bigl[\\partial_{\\gamma}, [\\partial_{\\alpha}, \\partial_{\\beta}]\\bigr] +
\n\\bigl[\\partial_{\\alpha}, [\\partial_{\\beta}, \\partial_{\\gamma}]\\bigr]+
\n\\bigl[\\partial_{\\beta}, [\\partial_{\\gamma}, \\partial_{\\alpha}]\\bigr]\\Bigr)\u00a0\\boldsymbol{e}_{\\nu} =0$$ \u3088\u308a<\/p>\n

\\begin{eqnarray}
\n&&R^{\\mu}_{\\ \\ \\ \\nu\\alpha\\beta, \\gamma} + R^{\\lambda}_{\\ \\ \\ \\nu\\alpha\\beta} \\Gamma^{\\mu}_{\\ \\ \\lambda\\gamma} -R^{\\mu}_{\\ \\ \\ \\lambda\\alpha\\beta} \\Gamma^{\\lambda}_{\\ \\ \\nu\\gamma} \\\\
\n&+& R^{\\mu}_{\\ \\ \\ \\nu\\beta\\gamma, \\alpha} + R^{\\lambda}_{\\ \\ \\ \\nu\\beta\\gamma} \\Gamma^{\\mu}_{\\ \\ \\lambda\\alpha} -R^{\\mu}_{\\ \\ \\ \\lambda\\beta\\gamma} \\Gamma^{\\lambda}_{\\ \\ \\nu\\alpha}\\\\
\n&+& R^{\\mu}_{\\ \\ \\ \\nu\\gamma\\alpha, \\beta} + R^{\\lambda}_{\\ \\ \\ \\nu\\gamma\\alpha} \\Gamma^{\\mu}_{\\ \\ \\lambda\\beta} -R^{\\mu}_{\\ \\ \\ \\lambda\\gamma\\alpha} \\Gamma^{\\lambda}_{\\ \\ \\nu\\beta} \\ \\ = \\ \\\u00a0 0
\n\\end{eqnarray} \u3053\u308c\u304c\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u306b\u5bfe\u3059\u308b\u300c\u30d3\u30a2\u30f3\u30ad\u6052\u7b49\u5f0f<\/strong><\/span>\u300d\u3067\u3042\u308b\u3002<\/p>\n

\\( \\alpha \\rightarrow \\mu\\) \u306b\u304b\u3048\u3066\u7e2e\u7d04\u3092\u3068\u308a\uff0c\u3055\u3089\u306b \\(g^{\\beta\\nu}\\) \u3082\u304b\u3051\u3066\u7e2e\u7d04\u3059\u308b\u3068\uff0c\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u3068\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc<\/strong><\/span>\u306b\u5bfe\u3059\u308b\u4ee5\u4e0b\u306e\u5f0f\u306b\u306a\u308b\u3002<\/p>\n

$$-2\\left( R^{\\mu}_{\\ \\ \\ \\gamma, \\mu} + \\Gamma^{\\mu}_{\\ \\ \\mu\\lambda} R^{\\lambda}_{\\ \\ \\ \\gamma} – \\Gamma^{\\lambda}_{\\ \\ \\mu\\gamma} R^{\\mu}_{\\ \\ \\ \\lambda}\\right) + R_{,\\gamma} = 0$$<\/p>\n

\u3053\u3053\u3067\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206 \\(G^{\\mu}_{\\ \\\u00a0 \\gamma}\\) \u3092\u4ee5\u4e0b\u306e\u5b9a\u7fa9\u3059\u308b\u3068\uff0c
\n$$G^{\\mu}_{\\ \\\u00a0 \\gamma} \\equiv R^{\\mu}_{\\ \\\u00a0 \\gamma} – \\frac{1}{2} \\delta^{\\mu}_{\\ \\\u00a0 \\gamma} R$$
\n\u7e2e\u7d04\u3055\u308c\u305f\u30d3\u30a2\u30f3\u30ad\u6052\u7b49\u5f0f<\/strong><\/span>\u306f\uff0c(1,1)-\u578b\u306e\u30c6\u30f3\u30bd\u30eb\uff0c\u3064\u307e\u308a\u4e0a\u6dfb\u5b571\u3064\u4e0b\u6dfb\u5b571\u3064\u306e\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306e\u5171\u5909\u5fae\u5206\u3092\u3064\u304b\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7c21\u6f54\u306b\u66f8\u3051\u308b\u3002
\n$$G^{\\mu}_{\\ \\ \\gamma; \\mu} = 0$$
\n\u6dfb\u5b57\u306e\u4e0a\u3052\u4e0b\u3052\u3068\u5171\u5909\u5fae\u5206\u306f\u53ef\u63db\u3067\u3042\u308b\u306e\u3067\uff08\u3053\u3053<\/a>\u3092\u53c2\u7167\uff09\uff0c\\( G^{\\mu\\nu} \\equiv g^{\\nu\\gamma} G^{\\mu}_{\\ \\ \\gamma}\\) \u306b\u5bfe\u3057\u3066
\n$$G^{\\mu\\nu}_{\\ \\\u00a0 \\\u00a0 ; \\nu} = 0$$\u3068\u3082\u66f8\u3051\u308b\u3002<\/p>\n

\u3053\u306e\u7d50\u679c\u304c\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u5de6\u8fba\u306b\u304a\u304f\u3079\u304d\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u304c\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u305d\u306e\u3082\u306e\u3067\u3082\u306a\u304f\uff0c\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u305d\u306e\u3082\u306e\u3067\u3082\u306a\u304f\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3067\u3042\u308b\u3079\u304d\u3060\u3068\u3044\u3046\uff0c\u4e00\u3064\u306e\u6307\u5c0e\u539f\u7406\u306b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n

\u3068\u3044\u3046\u306e\u3082\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306e\u53f3\u8fba\u306b\u306f\uff0c\u7269\u8cea\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb<\/strong><\/span> \\(T^{\\mu\\nu}\\) \u304c\u304f\u308b\u3053\u3068\u304c\u60f3\u5b9a\u3055\u308c\u308b\u304c\uff0c \\(T^{\\mu\\nu}\\) \u306f\u4ee5\u4e0b\u306e\u95a2\u4fc2\u3092\u6e80\u305f\u3059\u304b\u3089\u3067\u3042\u308b\u3002
\n$$T^{\\mu\\nu}_{\\ \\ \\ \\\u00a0 ; \\nu} = 0$$<\/p>\n

\u3053\u306e\u5f62\u306e\u4f55\u304c\u3046\u308c\u3057\u3044\u304b\u3068\u3044\u3046\u3068\uff0c\u3042\u308b\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206 \\(J^{\\mu}\\) \u306b\u5bfe\u3059\u308b\uff08\u5171\u5909\u5fae\u5206\u7684\uff09\u9023\u7d9a\u306e\u5f0f
\n$$J^{\\mu}_{\\ \\ \\ ; \\mu} = 0$$
\n\u306b\u5f62\u304c\u4f3c\u3066\u3044\u308b\u3053\u3068\uff0c\u305d\u3057\u3066\u9023\u7d9a\u306e\u5f0f\u306f\u300c\u4fdd\u5b58\u5247\u300d\u3092\u8868\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u3088\u308b\u3002<\/p>\n

\u3082\u3063\u3068\u3082\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206 \\(J^{\\mu}\\) \u306b\u5bfe\u3059\u308b\uff08\u5171\u5909\u5fae\u5206\u7684\uff09\u9023\u7d9a\u306e\u5f0f\u306f
\n$$J^{\\mu}_{\\ \\ \\ ; \\mu} = \\frac{1}{\\sqrt{-g}} \\left(\\sqrt{-g} J^{\\mu}\\right)_{, \\mu} = 0, \\quad\\therefore\\ \\ \\left(\\sqrt{-g} J^{\\mu}\\right)_{, \\mu} = 0$$
\n\u3068\u306a\u3063\u3066\uff0c\u78ba\u304b\u306b\u300c\u9023\u7d9a\u306e\u5f0f\u300d\u3068\u306a\u3063\u3066\u300c\u4fdd\u5b58\u5247\u300d\u3092\u8868\u3059\u304c\uff0c\u30c6\u30f3\u30bd\u30eb\u306e\u5834\u5408\u306f\u4e00\u822c\u306b\u306f\uff08\u30ad\u30ea\u30f3\u30b0\u30d9\u30af\u30c8\u30eb\u304c\u5b58\u5728\u3057\u306a\u3044\u9650\u308a\uff09\u300c\u4fdd\u5b58\u5247\u300d\u3092\u8868\u3059\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u3064\u307e\u308a\uff0c \\(T^{\\mu\\nu}_{\\ \\ \\\u00a0 \\ ; \\nu} = 0\\) \u3060\u304b\u3089\u3068\u3044\u3063\u3066\uff0c\u7269\u8cea\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3084\u904b\u52d5\u91cf\u304c\uff08\u5358\u4f53\u3067\uff09\u4fdd\u5b58\u3059\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u3002\uff08\u4e00\u77ac\uff0c\u3053\u308c\u306f\u4e00\u5927\u4e8b\uff01\u3068\u601d\u3063\u3066\u3057\u307e\u3046\u304c\uff0c\u305d\u306e\u3053\u3053\u308d\u306f\uff0c\u7269\u8cea\u5358\u4f53\u3067\u306f\u306a\u304f\uff0c\u7269\u8cea\u3068\u91cd\u529b\u5834\u306e\u5206\u3082\u3042\u308f\u305b\u305f\u5168\u4f53\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf\u304c\u4fdd\u5b58\u3059\u308b\u306f\u305a\u3060\uff0c\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002\uff09<\/p>\n

\u53c2\u8003\u307e\u3067\u306b\uff0c\u7e2e\u7d04\u3059\u308b\u524d\u306e\u30d3\u30a2\u30f3\u30ad\u6052\u7b49\u5f0f<\/strong><\/span>\u3092(1, 3)-\u578b\u30c6\u30f3\u30bd\u30eb\uff0c\u3064\u307e\u308a\u4e0a\u6dfb\u5b57\u304c1\u3064\uff0c\u4e0b\u6dfb\u5b57\u304c3\u3064\u306e\u30c6\u30f3\u30bd\u30eb\u306b\u5bfe\u3059\u308b\u5171\u5909\u5fae\u5206\u3092\u4f7f\u3063\u3066\u66f8\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002
\n$$R^{\\mu}_{\\ \\\u00a0 \\nu\\alpha\\beta; \\gamma}+R^{\\mu}_{\\ \\\u00a0 \\nu\\beta\\gamma; \\alpha} + R^{\\mu}_{\\ \\\u00a0 \\nu\\gamma\\alpha; \\beta} = 0$$<\/p>\n

\u3055\u3066\uff0c\u504f\u5fae\u5206\u306f \\( , \\) \u3067\u3042\u3089\u308f\u3059\u306e\u306b\u5bfe\u3057\u3066\uff0c\u5171\u5909\u5fae\u5206\u3092 \\(; \\) \u3067\u8868\u3057\u3066\u3044\u308b\u304c\uff0c\u5b9a\u7fa9\u306b\u3064\u3044\u3066\u306f\u3053\u3053<\/a>\u3092\u53c2\u7167\u3002<\/p>\n

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