<\/p>\n
4\u6b21\u5143\u6642\u7a7a\u306e\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306f\u5bfe\u79f0\u3067\u3042\u308a\uff0c\u5bfe\u79f0\u306a4\u6b21\u6b63\u65b9\u884c\u5217\u3068\u307f\u306a\u305b\u308b\u3002<\/p>\n
$$g_{\\mu\\nu} = g_{\\nu\\mu}$$<\/p>\n
\u305f\u3068\u3048\u3070\uff0c$g_{12} = g_{21}$ \u306a\u306e\u3067\uff0c2\u3064\u306e\u6210\u5206 $g_{12},\\, g_{21}$ \u306b\u3064\u3044\u3066\u306f\uff0c\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u3068\u3057\u3066\u306f $2$ \u3067\u306f\u306a\u304f $1$ \u3068\u306a\u308b\u3002\u3067\u306f\uff0c4\u6b21\u5143\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u306f\u4f55\u500b\u304b\uff1f<\/p>\n
\\begin{eqnarray}
\ng_{\\mu\\nu} &=&
\n\\left( \\begin{array}{cccc}g_{00} & {\\color{yellow}g_{01}} & {\\color{yellow}g_{02}} & {\\color{yellow}g_{03}} \\\\
\ng_{10} & g_{11} & {\\color{yellow}g_{12}} & {\\color{yellow}g_{13}} \\\\
\ng_{20} & g_{21} & g_{22} & {\\color{yellow}g_{23}} \\\\
\ng_{30} & g_{31} & g_{32} & g_{33}
\n\\end{array} \\right)
\n\\end{eqnarray}<\/p>\n
\u6b21\u306e\u52d5\u753b\u3092\u898b\u3066\uff0c\u5bfe\u79f0\u306a $n$ \u6b21\u6b63\u65b9\u884c\u5217\u306e\u72ec\u7acb\u306a\u6210\u5206\u306e\u500b\u6570\u3092 $n$ \u3067\u8868\u305b\u3002\uff08$n=4$ \u306e\u5834\u5408\u306f\u554f\u984c 1 \u306e\u7b54\u3048\u306b\u306a\u308b\u3053\u3068\u3082\u78ba\u8a8d\u3059\u308b\u3093\u3067\u3059\u3088\u3002\uff09<\/p>\n