{"id":337,"date":"2022-01-06T17:52:18","date_gmt":"2022-01-06T08:52:18","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=337"},"modified":"2022-02-18T16:42:31","modified_gmt":"2022-02-18T07:42:31","slug":"%e5%b9%b3%e8%a1%8c%e7%b7%9a%e3%81%ae%e5%85%ac%e7%90%86%e3%81%ae%e7%a0%b4%e3%82%8c%e3%81%a8%e3%83%aa%e3%83%bc%e3%83%9e%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab","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\/%e5%b9%b3%e8%a1%8c%e7%b7%9a%e3%81%ae%e5%85%ac%e7%90%86%e3%81%ae%e7%a0%b4%e3%82%8c%e3%81%a8%e3%83%aa%e3%83%bc%e3%83%9e%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab\/","title":{"rendered":"\u5e73\u884c\u7dda\u306e\u516c\u7406\u306e\u7834\u308c\u3068\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb"},"content":{"rendered":"

\u6642\u7a7a\u304c\u66f2\u304c\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u77e5\u308b\u305f\u3081\u306b\u306f\uff0c\u66f2\u304c\u3063\u3066\u3044\u306a\u3044\uff0c\u3064\u307e\u308a\u5e73\u5766\u306a\u6642\u7a7a\u3067\u6210\u308a\u7acb\u3064\u300c\u5e73\u884c\u7dda\u306e\u516c\u7406<\/strong><\/span>\u300d\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u8abf\u3079\u308b\u3053\u3068\u304c\u624b\u304c\u304b\u308a\u3068\u306a\u308b\u3002<\/p>\n

2\u672c\u306e\u8fd1\u63a5\u6e2c\u5730\u7dda<\/h3>\n

\u307e\u305a\uff0c\u300c\u307e\u3063\u3059\u3050\u306a\u7dda<\/strong><\/span>\u300d\u3067\u3042\u308b\u6e2c\u5730\u7dda<\/strong><\/span>\u30922\u672c\u7528\u610f\u3059\u308b\u3002<\/p>\n

\u305d\u308c\u305e\u308c\u306e\u4e16\u754c\u7dda<\/strong><\/span>\u3092 \\(x^{\\mu}(v)\\), \\(\\tilde{x}^{\\mu}(v) \\) \u3068\u8868\u3059\u3068\uff0c\u305d\u308c\u305e\u308c\u306e\u63a5\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u306f
\n$$\\boldsymbol{u} (x)= u^{\\mu}(x) \\boldsymbol{e}_{\\mu}(x) = \\frac{dx^{\\mu}}{dv} \\boldsymbol{e}_{\\mu}(x)$$
\n$$\\tilde{\\boldsymbol{u}} (\\tilde{x}) = \\tilde{u}^{\\mu}(\\tilde{x}) \\boldsymbol{e}_{\\mu}(\\tilde{x}) = \\frac{d\\tilde{x}^{\\mu}}{dv} \\boldsymbol{e}_{\\mu}(\\tilde{x})$$
\n\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f<\/strong><\/span>\u306f
\n\\begin{equation}
\n\\frac{d\\boldsymbol{u}}{dv} = \\boldsymbol{0},
\n\\quad
\n\\frac{d\\tilde{\\boldsymbol{u}}}{dv} = \\boldsymbol{0}
\n\\end{equation}
\n\u3067\u3042\u308b\u3002<\/p>\n

\u7279\u306b\u3053\u308c\u30892\u672c\u306e\u6e2c\u5730\u7dda\u304c\u8fd1\u63a5\u3057\u3066\u3044\u308b\u3068\u3057\u3066\uff0c
\n$$\\tilde{x}^{\\mu}(v)=x^{\\mu}(v) + \\epsilon\\, \\xi^{\\mu}, \\quad |\\epsilon| \\ll 1$$
\n\u3068\u304a\u304d\uff0c\u5fae\u5c0f\u91cf \\(\\epsilon\\) \u306e1\u6b21\u307e\u3067\u3068\u308b\u3068\uff0c<\/p>\n

\\begin{eqnarray}
\n\\tilde{\\boldsymbol{u}} &=&
\n\\left( \\frac{dx^{\\mu}}{dv} + \\epsilon \\frac{d\\xi^{\\mu}}{dv}\\right) \\boldsymbol{e}_{\\mu}(x + \\epsilon \\xi)\\\\
\n&\\simeq&\\left( \\frac{dx^{\\mu}}{dv} + \\epsilon \\frac{d\\xi^{\\mu}}{dv}\\right)
\n\\left( \\boldsymbol{e}_{\\mu}+ \\epsilon\\, \\boldsymbol{e}_{\\mu, \\nu} \\xi^{\\nu}\\right)\\\\
\n&\\simeq& \\boldsymbol{u}(x) + \\epsilon\\,\\frac{d\\xi^{\\mu}}{dv} \\boldsymbol{e}_{\\mu}
\n+ \\epsilon\\, \\frac{dx^{\\mu}}{dv} \\boldsymbol{e}_{\\color{red}{\\mu, \\nu}} \\xi^{\\nu}\\\\
\n&=& \\boldsymbol{u}(x) + \\epsilon\\,\\frac{d\\xi^{\\mu}}{dv} \\boldsymbol{e}_{\\mu}
\n+ \\epsilon\\,\u00a0 \\xi^{\\nu}\\boldsymbol{e}_{\\color{red}{\\nu, \\mu}}\\frac{dx^{\\mu}}{dv}\\\\
\n&=& \\boldsymbol{u}(x) + \\epsilon \\frac{d}{dv}\\left( \\xi^{\\nu} \\boldsymbol{e}_{\\nu}\\right)
\n\\end{eqnarray}<\/p>\n

\u4e00\u65b9\uff0c\\(\\tilde{\\boldsymbol{u}} = \\boldsymbol{u} (\\tilde{x}) = \\boldsymbol{u}({x} + \\epsilon\\, \\xi)\\) \u3067\u3042\u308b\u304b\u3089\uff0c\u5fae\u5c0f\u91cf \\(\\epsilon\\) \u306e1\u6b21\u307e\u3067\u3068\u308b\u3068\uff0c<\/p>\n

$$ \\tilde{\\boldsymbol{u}}=\\boldsymbol{u} ({x} + \\epsilon\\, \\xi)
\n\\simeq \\boldsymbol{u}(x) + \\epsilon\\, \\boldsymbol{u}_{ , \\mu} \\xi^{\\mu}$$<\/p>\n

\\(\\epsilon\\) \u306e1\u6b21\u306e\u9805\u3092\u7b49\u3057\u3044\u3068\u304a\u304f\u3068<\/p>\n

$$ \\frac{d}{dv}\\left( \\xi^{\\mu} \\boldsymbol{e}_{\\mu}\\right) = \\boldsymbol{u}_{ , \\mu} \\xi^{\\mu}$$ \u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n

\u504f\u5dee\u30d9\u30af\u30c8\u30eb<\/h3>\n

\u3053\u3053\u3067\uff0c\\( \\xi^{\\mu}\\) \u3092\u6210\u5206\u3068\u3059\u308b\u30d9\u30af\u30c8\u30eb<\/p>\n

$$\\boldsymbol{\\xi}\\equiv \\xi^{\\mu} \\boldsymbol{e}_{\\mu}$$
\n\u3092\u5c0e\u5165\u3059\u308b\u3002\\(\\boldsymbol{\\xi}\\) \u306f\uff082\u672c\u306e\u8fd1\u63a5\u6e2c\u5730\u7dda\u306e\u5dee\u3092\u8868\u3059\u306e\u3067\uff09\u504f\u5dee\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\uff08deviation vector<\/strong><\/span>\uff09\u3068\u304b\uff082\u672c\u306e\u8fd1\u63a5\u6e2c\u5730\u7dda\u3092\u9023\u7d50\u3055\u305b\u308b\u306f\u305f\u3089\u304d\u304c\u3042\u308b\u306e\u3067\uff09\u9023\u7d50\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\uff08connecting vector<\/strong><\/span>\uff09\u306a\u3069\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u3002<\/p>\n

\u4e0a\u3067\u5f97\u3089\u308c\u305f\u7d50\u679c\u304b\u3089\uff0c
\n$$ \\frac{d\\boldsymbol{\\xi}}{dv} = \\boldsymbol{u}_{, \\nu}\\, \\xi^{\\nu}\u00a0$$<\/p>\n

\u3061\u306a\u307f\u306b\uff0c\u5225\u30da\u30fc\u30b8<\/a>\u3067\u8ff0\u3079\u308b\u3088\u3046\u306b\u30a2\u30d5\u30a3\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf<\/strong><\/span>\u3068\u3057\u3066 \\(v\\) \u306e\u304b\u308f\u308a\u306b\u56fa\u6709\u6642\u9593<\/strong><\/span> \\(\\tau\\) \u3092\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u3066\uff0c\u305d\u306e\u3088\u3046\u306b\u3068\u308b\u3068\u6e2c\u5730\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{u}\\) \u3068\u504f\u5dee\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{\\xi}\\) \u306e\u5185\u7a4d\u306f\uff0c\u6e2c\u5730\u7dda\u306b\u6cbf\u3063\u3066\u4e00\u5b9a\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u306a\u305c\u306a\u3089\u3070\uff0c<\/p>\n

\\begin{eqnarray}
\n\\frac{d}{d\\tau}\\left(\\boldsymbol{u}\\cdot\\boldsymbol{\\xi} \\right) &=&
\n\\frac{d\\boldsymbol{u}}{d\\tau}\\cdot\\boldsymbol{\\xi} + \\boldsymbol{u}\\cdot\\frac{d\\boldsymbol{\\xi}}{d\\tau}\\\\
\n&=& \\boldsymbol{0}\\cdot\\boldsymbol{\\xi} + \\boldsymbol{u}\\cdot\\boldsymbol{u}_{, \\mu}\\, \\xi^{\\mu}\\\\
\n&=& \\frac{1}{2} (\\boldsymbol{u}\\cdot\\boldsymbol{u})_{, \\mu}\\, \\xi^{\\mu}\\\\
\n&=& 0 \\quad \\because\\ \\ \\boldsymbol{u}\\cdot\\boldsymbol{u} = -c^2
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u3053\u3068\u3092\u4f7f\u3046\u3068\uff0c\u504f\u5dee\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{\\xi}\\) \u306f\uff0c\u5e38\u306b\u6e2c\u5730\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{u}\\) \u306b\u76f4\u4ea4\u3059\u308b\u3088\u3046\u306b\u8a2d\u5b9a\u3067\u304d\u308b\u3053\u3068\u3082\u660e\u3089\u304b\u3067\u3059\u306d\u3002\uff08\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066 \\(\\boldsymbol{u}\\cdot\\boldsymbol{\\xi}=0\\) \u3068\u3059\u308c\u3070\uff0c\u305a\u30fc\u3063\u3068\\(\\boldsymbol{u}\\cdot\\boldsymbol{\\xi}=0\\) \u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\uff09<\/p>\n

\u6e2c\u5730\u7dda\u504f\u5dee\u65b9\u7a0b\u5f0f\u3068\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/h3>\n

\u3055\u3089\u306b\u3082\u3046\u4e00\u968e\u5fae\u5206\u3059\u308b\u3068\uff0c\u4ee5\u4e0b\u306e\u5f0f\u304c\u5f97\u3089\u308c\u308b\u3002\uff08\u8a08\u7b97\u306e\u8a73\u7d30\u306f\u88dc\u8db3<\/a>\u3067\u3002\uff09
\n\\begin{equation}
\n\\frac{d^2\\boldsymbol{\\xi}}{dv^2} =
\n\\left(\\boldsymbol{e}_{\\mu,\\rho\\nu} – \\boldsymbol{e}_{\\mu,\\nu\\rho}\\right)
\nu^{\\mu}u^{\\nu}\\xi^{\\rho}.
\n\\end{equation}
\n\u3053\u306e\u5f0f\u306e\u5de6\u8fba\u306f\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\uff0c\u3059\u3079\u304b\u3089\u304f\u30d9\u30af\u30c8\u30eb\u306f\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u7dda\u5f62\u7d50\u5408\u3067\u66f8\u304b\u308c\u308b\u306e\u3067\u3042\u308b\u304b\u3089\uff0c\u53f3\u8fba\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e2\u968e\u5fae\u5206\u3067\u3042\u308b \\((\\boldsymbol{e}_{\\mu,\\rho\\nu} – \\boldsymbol{e}_{\\mu,\\nu\\rho})\\) \u3082\u307e\u305f\uff0c\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306e\u7dda\u5f62\u7d50\u5408\u3067\u66f8\u304b\u308c\u308b\u306f\u305a\u3060\u3002<\/p>\n

\u305d\u3053\u3067\uff0c
\n\\begin{equation}\\label{eq:rie1}
\n\\boldsymbol{e}_{\\mu,\\rho\\nu} – \\boldsymbol{e}_{\\mu,\\nu\\rho}
\n\\equiv R^{\\sigma}_{\\ \\ \\mu\\nu\\rho} \\boldsymbol{e}_{\\sigma}
\n\\end{equation}
\n\u3068\u66f8\u304f\u3002\\(R^{\\sigma}_{\\ \\ \\mu\\nu\\rho}\\)\u306f\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u306e\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong>\u306e\u6210\u5206<\/span>\u3092\u4f7f\u3063\u3066\u66f8\u304d\u76f4\u3059\u3068\uff0c
\n\\begin{equation}
\n\\frac{d^2\\boldsymbol{\\xi}}{dv^2} =
\nR^{\\sigma}_{\\ \\mu\\nu\\rho}\\,u^{\\mu}u^{\\nu}\\xi^{\\rho}\\,\\boldsymbol{e}_{\\sigma}
\n\\end{equation}
\n\u3068\u306a\u308b\u3002\u3053\u306e\u5f0f\u306f2\u672c\u306e\u6e2c\u5730\u7dda\u9593\u306e\u9593\u9694\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u6c7a\u3081\u308b\u5927\u5207\u306a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c\u6e2c\u5730\u7dda\u504f\u5dee\u65b9\u7a0b\u5f0f<\/strong><\/span>\uff08\u307e\u305f\u306f\u5358\u306b\u6e2c\u5730\u7dda\u504f\u5dee\u306e\u5f0f<\/strong><\/span>\u306a\u3069\uff09\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u3002<\/p>\n

 <\/p>\n

\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u5f79\u5272<\/h3>\n

\u3082\u3057\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u5168\u3066\u306e\u6210\u5206\u304c\u30bc\u30ed\u3060\u3068\u3059\u308b\u3068\uff0c\u305d\u306e\u6642\u7a7a\u3067\u306f\u6e2c\u5730\u7dda\u504f\u5dee\u306e\u5f0f<\/strong><\/span>\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002
\n\\begin{equation}\\label{eq:flat}
\nR^{\\sigma}_{\\ \\mu\\nu\\rho} = 0 \\ \\Rightarrow\\
\n\\frac{d^2\\boldsymbol{\\xi}}{dv^2} =\\boldsymbol{0}
\n\\end{equation}
\n\u3059\u308b\u3068\uff0c\u4f8b\u3048\u3070 \\(v = v_0\\) \u3067
\n\\begin{equation}
\n\\frac{d\\boldsymbol{\\xi}}{dv}\\biggr|_{v_0} =\\boldsymbol{0}
\n\\end{equation}
\n\u3064\u307e\u308a\uff0c\u521d\u671f\u8a2d\u5b9a\u3068\u3057\u3066\u9593\u9694\u3092\u4e00\u5b9a\u306b\u3057\u305f2\u672c\u306e\u8fd1\u63a5\u6e2c\u5730\u7dda\u3092\u6e96\u5099\u3057\u3066\u3084\u308b\u3068\uff0c\u6e2c\u5730\u7dda\u504f\u5dee\u306e\u5f0f<\/strong><\/span>\u306b\u3088\u308a\uff0c\u4efb\u610f\u306e \\(v\\) \u306b\u3064\u3044\u3066
\n\\begin{equation}
\n\\frac{d\\boldsymbol{\\xi}}{dv} =\\boldsymbol{0}
\n\\end{equation}
\n\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3064\u307e\u308a\uff0c\\(R^{\\sigma}_{\\ \\mu\\nu\\rho} = 0\\) \u3067\u3042\u308b\u6642\u7a7a\u3067\u306f\uff0c\u6700\u521d\uff0c\u5e73\u884c\u306b\u304a\u3044\u305f2\u672c\u306e\u300c\u307e\u3063\u3059\u3050\u306a\u7dda<\/strong><\/span>\u300d\u306f\u3069\u3053\u307e\u3067\u4f38\u3070\u3057\u3066\u3044\u3063\u3066\u3082\u9593\u9694\u304c\u4e00\u5b9a\u3067\u3042\u308a\u6c7a\u3057\u3066\u4ea4\u308f\u3089\u306a\u3044\u3002<\/p>\n

\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u5168\u3066\u306e\u6210\u5206\u304c\u30bc\u30ed\u3067\u3042\u308b\u6642\u7a7a\u3068\u306f\uff0c\u5e73\u884c\u7dda\u304c\u3069\u3053\u307e\u3067\u3044\u3063\u3066\u3082\u6587\u5b57\u901a\u308a\u300c\u5e73\u884c\u7dda\u3092\u305f\u3069\u308b\u3088\u3046\u306a\u300d\u6642\u7a7a\uff0c\u3064\u307e\u308a\u5e73\u884c\u7dda\u306e\u516c\u7406\u304c\u6210\u308a\u7acb\u3064\u5e73\u5766\u306a\uff08\u66f2\u304c\u3063\u3066\u3044\u306a\u3044\uff09\u6642\u7a7a\u306a\u306e\u3067\u3042\u308b\u3002<\/strong><\/span><\/p>\n

\u9006\u306b\uff0c\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u304c\u30bc\u30ed\u3067\u306a\u3044\u6642\u7a7a\u3067\u306f\uff0c\u305f\u3068\u3048\u6700\u521d\u306b\u5e73\u884c\u306a2\u672c\u306e\u6e2c\u5730\u7dda\u3092\u8a2d\u5b9a\u3057\u305f\u3068\u3057\u3066\u3082\uff0c2\u672c\u306e\u9593\u9694\u306f\u4e00\u5b9a\u3067\u306f\u306a\u304f\u306a\u308b\u3002\u3069\u3093\u3069\u3093\u4f38\u3070\u3057\u3066\u3044\u3051\u3070\uff0c\u3084\u304c\u3066\u305d\u306e\u9593\u9694\u304c\u5909\u5316\u3057\uff0c\u3042\u308b\u5834\u5408\u306b\u306f\u4ea4\u308f\u3063\u3066\u3057\u307e\u3063\u305f\u308a\uff0c\u307e\u305f\u3042\u308b\u5834\u5408\u306b\u306f\u96e2\u308c\u3066\u3044\u3063\u3066\u3057\u307e\u3046\u3060\u308d\u3046\u3002<\/p>\n

\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u306f\uff0c\u305d\u306e\u6642\u7a7a\u306b\u304a\u3051\u308b\u5e73\u884c\u7dda\u306e\u516c\u7406\u306e\u7834\u308c\u5177\u5408\uff0c<\/strong><\/span>
\n\u3064\u307e\u308a\u305d\u306e\u6642\u7a7a\u306e\u66f2\u304c\u308a\u5177\u5408\u3092\u8868\u3059\u91cf\u306a\u306e\u3067\u3042\u308b\u3002<\/strong><\/span><\/p>\n

\u6b21\u306b\u9032\u3080\u524d\u306b\uff0c\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306f\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7<\/strong><\/span>\uff08\u3068\u305d\u306e1\u968e\u5fae\u5206\uff09\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u304a\u3053\u3046\u3002<\/p>\n

\u57fa\u672c\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u306e1\u968e\u5fae\u5206\u306f\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7<\/strong><\/span>\u3067\u66f8\u304b\u308c\u308b\u3002\u3053\u308c\u3092\u4ee3\u5165\u3059\u308c\u3070\uff0c\u4ee5\u4e0b\u304c\u5f97\u3089\u308c\u308b\u3002\uff08\u8a73\u7d30\u306f\u88dc\u8db3<\/a>\u3067\u3002\uff09
\n\\begin{eqnarray}
\nR^{\\sigma}_{\\ \\ \\mu\\nu\\rho} &=& \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho,\\nu} –
\n\\varGamma^{\\sigma}_{\\ \\ \\mu\\nu,\\rho} \\nonumber + \\varGamma^{\\sigma}_{\\ \\ \\lambda\\nu}\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}
\n– \\varGamma^{\\sigma}_{\\ \\ \\lambda\\rho}\\varGamma^{\\lambda}_{\\ \\ \\mu\\nu}.
\n\\end{eqnarray}
\n\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7<\/strong><\/span>\u304c\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u306e1\u968e\u504f\u5fae\u5206\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u305b\u3070\uff0c\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u306f\uff0c\u6700\u7d42\u7684\u306b\u306f\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u306e\u6210\u5206\u306e2\u968e\u504f\u5fae\u5206\u307e\u3067\u3092\u542b\u3080\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":67,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-337","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=337"}],"version-history":[{"count":46,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/337\/revisions"}],"predecessor-version":[{"id":1991,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/337\/revisions\/1991"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/67"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}