Python \u306e EinsteinPy \u3084 Maxima \u306e ctensor \u306a\u3069\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4ee3\u6570\u30b7\u30b9\u30c6\u30e0\u3092\u4f7f\u3063\u3066\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6c42\u3081\u308b\u4f8b\u3002<\/p>\n
<\/p>\n
\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3044\u3046\u306e\u306f\u3069\u3046\u3044\u3046\u3053\u3068\u304b\uff0c\u3068\u3044\u3046\u3068…<\/p>\n
\\begin{eqnarray}
\nds^2 &=&\u00a0 g_{\\mu\\nu}\\,dx^{\\mu}dx^{\\nu}.
\n\\end{eqnarray}<\/p>\n
\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb \\(g_{\\mu\\nu}\\) \u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f\u6700\u592710\u500b\uff0c\u305d\u308c\u305e\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e\u6700\u59274\u5909\u6570\u306b\u4f9d\u5b58\u3059\u308b\u95a2\u6570\u3002<\/p>\n
\\begin{equation}
\n\\varGamma^{\\lambda}_{\\ \\ \\mu\\nu} = \\frac{1}{2} g^{\\lambda\\sigma}
\n\\left(g_{\\sigma\\mu,\\nu} + g_{\\sigma\\nu,\\mu} \u2013 g_{\\mu\\nu,\\sigma}
\n\\right)
\n\\end{equation}<\/p>\n
\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f40\u500b\uff0c40\u500b\u305d\u308c\u305e\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e4\u5909\u6570\u95a2\u6570\u3002<\/p>\n
\\begin{eqnarray}
\nR^{\\sigma}_{\\ \\ \\mu\\nu\\rho} &=& \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho,\\nu} \u2013
\n\\varGamma^{\\sigma}_{\\ \\ \\mu\\nu,\\rho} \\nonumber + \\varGamma^{\\sigma}_{\\ \\ \\lambda\\nu}\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}
\n\u2013 \\varGamma^{\\sigma}_{\\ \\ \\lambda\\rho}\\varGamma^{\\lambda}_{\\ \\ \\mu\\nu}.
\n\\end{eqnarray}<\/p>\n
\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f20\u500b\uff0c20\u500b\u305d\u308c\u305e\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e4\u5909\u6570\u95a2\u6570\u3002<\/p>\n
\\begin{equation}
\nR_{\\mu\\rho} \\equiv R^{\\nu}_{\\ \\ \\mu\\nu\\rho} =R_{\\rho\\mu} .
\n\\end{equation}<\/p>\n
\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f10\u500b\uff0c10\u500b\u305d\u308c\u305e\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e4\u5909\u6570\u95a2\u6570\u3002<\/p>\n
\\begin{equation}
\nR \\equiv g^{\\mu\\rho} R_{\\mu\\rho}
\n\\end{equation}<\/p>\n
\u30b9\u30ab\u30e9\u30fc\u3060\u304b\u30891\u500b\uff0c\u3053\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e4\u5909\u6570\u95a2\u6570\u3002<\/p>\n
$$G_{\\mu\\nu} \\equiv R_{\\mu\\nu} \u2013 \\frac{1}{2}g_{\\mu\\nu}\\, R = G_{\\nu\\mu}$$<\/p>\n
\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb\u3068\u540c\u69d8\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f10\u500b\uff0c10\u500b\u305d\u308c\u305e\u308c\u304c\u4e00\u822c\u306b\u5ea7\u6a19 \\(x^{\\mu}\\) \u306e4\u5909\u6570\u95a2\u6570\u3002<\/p>\n
\\begin{equation}
\nG_{\\mu\\nu} = \\frac{8\\pi G}{c^4}T_{\\mu\\nu}.
\n\\end{equation}<\/p>\n
\u5b87\u5b99\u5b9a\u6570 \\(\\Lambda\\) \u304c\u3042\u308b\u5834\u5408\u306b\u306f<\/p>\n
\\begin{equation}
\nG_{\\mu\\nu} + \\Lambda g_{\\mu\\nu}= \\frac{8\\pi G}{c^4}T_{\\mu\\nu}.
\n\\end{equation}<\/p>\n
\u3053\u3053\u3067 $T_{\\mu\\nu}$ \u306f\u7269\u8cea\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u3002<\/p>\n
\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f\u300c4\u5909\u6570\u95a2\u657010\u500b\u306b\u5bfe\u3059\u308b10\u5143\u9023\u7acb\u975e\u7dda\u5f62\uff08\u504f\u5fae\u5206\u306e\u968e\u6570\u304c\uff092\u968e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f10\u672c\u30ef\u30f3\u30bb\u30c3\u30c8\u300d\u3002<\/p>\n
… \u3068\u3044\u3046\u3075\u3046\u306b\uff0c\u3082\u306e\u3059\u3054\u3044\u8a08\u7b97\u91cf\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u3053\u308c\u3060\u3068\u6c42\u3081\u308b\u306e\u304c\u5927\u5909\u3067\uff0c\u307b\u307c\u4e0d\u53ef\u80fd\u306a\u306e\u3067\uff0c\u306a\u3093\u3089\u304b\u306e\u7c21\u5358\u5316\u30fb\u5358\u7d14\u5316\u3092\u304a\u3053\u306a\u3063\u3066\uff0c\u6c42\u3081\u308b\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306e\u500b\u6570\u3092\u306a\u308b\u3079\u304f\u6e1b\u3089\u3057\uff0c\u5bfe\u79f0\u6027\u306e\u4eee\u5b9a\u3092\u3057\u3066\u5ea7\u6a19\u4f9d\u5b58\u6027\u3092\u306a\u308b\u3079\u304f\u6e1b\u3089\u3057\u3066\uff08\u53ef\u80fd\u3067\u3042\u308c\u30701\u5909\u6570\u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u3088\u3046\u306b\u3067\u304d\u308c\u3070\uff0c\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u306f\u306a\u304f\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u306a\u308b\u306e\u3067\uff0c\u89e3\u304d\u3084\u3059\u304f\u306a\u308b\u304b\u3082\uff09\u3068\u3082\u304b\u304f\uff0c\u4eba\u9593\u304c\u89e3\u3051\u308b\u7a0b\u5ea6\u306e\u7c21\u5358\u306a\u5f62\u306b\u3059\u308b\u3002<\/p>\n
\u305d\u308c\u3067\u3082\uff0c\u4eba\u529b\u306e\u307f\u306b\u983c\u308b\u306e\u3067\u306f\u5927\u5909\u3060\u304b\u3089\uff0c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4ee3\u6570\u30b7\u30b9\u30c6\u30e0\u3092\u6d3b\u7528\u3057\u3066\u307f\u308b\u3002<\/p>\n
\u53c2\u8003\uff1a<\/p>\n