{"id":401,"date":"2022-01-07T14:06:30","date_gmt":"2022-01-07T05:06:30","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=401"},"modified":"2024-11-11T15:57:10","modified_gmt":"2024-11-11T06:57:10","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%83%aa%e3%83%bc%e3%83%9e%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab%e3%82%92%e3%82%af%e3%83%aa%e3%82%b9%e3%83%88%e3%83%83%e3%83%95%e3%82%a7%e3%83%ab%e8%a8%98%e5%8f%b7","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\/%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%83%aa%e3%83%bc%e3%83%9e%e3%83%b3%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab%e3%82%92%e3%82%af%e3%83%aa%e3%82%b9%e3%83%88%e3%83%83%e3%83%95%e3%82%a7%e3%83%ab%e8%a8%98%e5%8f%b7\/","title":{"rendered":"\u88dc\u8db3\uff1a\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb\u3092\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7\u3067\u8868\u3059"},"content":{"rendered":"

\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7<\/strong><\/span>\u306e\u5b9a\u7fa9
\n$$ \\boldsymbol{e}_{\\mu, \\nu} \\equiv \\varGamma^{\\lambda}_{\\ \\ \\mu\\nu} \\boldsymbol{e}_{\\lambda}$$
\n\u3068\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb<\/strong>\u306e\u6210\u5206<\/span>\u306e\u5b9a\u7fa9
\n\\begin{equation}
\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\u304b\u3089\uff0c\u4ee5\u4e0b\u3092\u5c0e\u304f\u3002
\n\\begin{eqnarray}
\nR^{\\sigma}_{\\ \\ \\mu\\nu\\rho} &=& \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho,\\nu} –
\n\\varGamma^{\\sigma}_{\\ \\ \\mu\\nu,\\rho} \\nonumber\u00a0 + \\varGamma^{\\sigma}_{\\ \\ \\lambda\\nu}\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}
\n– \\varGamma^{\\sigma}_{\\ \\ \\lambda\\rho}\\varGamma^{\\lambda}_{\\ \\ \\mu\\nu}
\n\\end{eqnarray}<\/p>\n

\n

\\begin{eqnarray}
\n\\boldsymbol{e}_{\\mu,\\rho\\nu} – \\boldsymbol{e}_{\\mu,\\nu\\rho}
\n&=& \\left( \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho} \\boldsymbol{e}_{\\sigma}\\right)_{, \\nu}
\n\\quad – \\quad \\left( \\varGamma^{\\sigma}_{\\ \\ \\mu\\nu} \\boldsymbol{e}_{\\sigma}\\right)_{, \\rho}\\\\
\n&=& \\quad \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho, \\nu}\\boldsymbol{e}_{\\sigma}
\n\\quad – \\quad\u00a0 \\varGamma^{\\sigma}_{\\ \\ \\mu\\nu, \\rho}\\boldsymbol{e}_{\\sigma} \\\\
\n&&+\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}\\boldsymbol{e}_{\\lambda, \\nu}
\n\\quad – \\quad \\varGamma^{\\lambda}_{\\ \\ \\mu\\nu}\\boldsymbol{e}_{\\lambda, \\rho}\\\\
\n&=& \\quad \\varGamma^{\\sigma}_{\\ \\ \\mu\\rho, \\nu}\\boldsymbol{e}_{\\sigma}
\n\\quad – \\quad\u00a0 \\varGamma^{\\sigma}_{\\ \\ \\mu\\nu, \\rho}\\boldsymbol{e}_{\\sigma} \\\\
\n&&+\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}\\varGamma^{\\sigma}_{\\ \\ \\lambda\\nu}\\boldsymbol{e}_{\\sigma}
\n\\quad – \\quad \\varGamma^{\\lambda}_{\\ \\ \\mu\\nu}\\varGamma^{\\sigma}_{\\ \\ \\lambda\\rho}\\boldsymbol{e}_{\\sigma}\\\\
\n&=& \\left(\\varGamma^{\\sigma}_{\\ \\ \\mu\\rho,\\nu} –
\n\\varGamma^{\\sigma}_{\\ \\ \\mu\\nu,\\rho} \\nonumber\u00a0 + \\varGamma^{\\sigma}_{\\ \\ \\lambda\\nu}\\varGamma^{\\lambda}_{\\ \\ \\mu\\rho}
\n– \\varGamma^{\\sigma}_{\\ \\ \\lambda\\rho}\\varGamma^{\\lambda}_{\\ \\ \\mu\\nu} \\right) \\boldsymbol{e}_{\\sigma}\\\\
\n&\\equiv& R^{\\sigma}_{\\ \\ \\mu\\nu\\rho} \\boldsymbol{e}_{\\sigma}
\n\\end{eqnarray}
\n\u3088\u308a\uff0c\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":337,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-401","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t