\u5225\u30da\u30fc\u30b8<\/strong><\/span><\/a>\u306b\u66f8\u3044\u305f\u3002<\/p>\n\\begin{eqnarray}
\nr &\\equiv& t \\sinh \\chi \\\\
\n\\tau &\\equiv& t \\cosh \\chi
\n\\end{eqnarray}<\/p>\n
\u4ee5\u4e0b\u306f\u6388\u696d\u306e\u7df4\u7fd2\u554f\u984c\u3068\u3057\u3066\u51fa\u3057\u305f\u3082\u306e\u3002<\/p>\n
\n\u30df\u30eb\u30f3\u5b87\u5b99\u306e\u8a08\u91cf\u306f\uff0c\u4e00\u69d8\u7b49\u65b9\u306a\u7a7a\u9593\u90e8\u5206\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u308b\u3002<\/p>\n
$$ds^2 = -dt^2 + t^2 \\left(\\frac{dr^2}{1 + r^2} + r^2 d\\Omega^2 \\right) $$<\/p>\n
\u3053\u308c\u3092\u5ea7\u6a19\u5909\u63db\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u8a08\u91cf\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n
$$ds^2 = -d\\tau^2 +dR^2 + R^2 d\\Omega^2$$<\/p>\n
\u5ea7\u6a19\u5909\u63db\u306f<\/p>\n
\\begin{eqnarray}
\nR &\\equiv& t\\, r \\\\
\n\\tau &\\equiv& t\\, \\sqrt{1 + r^2}
\n\\end{eqnarray}<\/p>\n
\u5fae\u5206\u3057\u3066<\/p>\n
\\begin{eqnarray}
\ndR &=& r dt + t dr \\tag{1}\\\\
\nd\\tau &=&\u00a0 \\sqrt{1 + r^2} \\,dt + t \\frac{r}{\\sqrt{1 + r^2}} dr \\tag{2}
\n\\end{eqnarray}<\/p>\n
\\(\\displaystyle (2) – (1)\\times \\frac{r}{\\sqrt{1+r^2}} \\) \u304b\u3089<\/p>\n
$$d\\tau – \\frac{r}{\\sqrt{1 + r^2}} dR =\\frac{1}{\\sqrt{1 + r^2}} dt$$<\/p>\n
\\(\\displaystyle (1) – (2)\\times \\frac{r}{\\sqrt{1+r^2}} \\) \u304b\u3089<\/p>\n
$$dR – \\frac{r}{\\sqrt{1 + r^2}} d\\tau =\\frac{t}{1 + r^2} dr$$<\/p>\n
\u3053\u308c\u3089\u3092\u4ee3\u5165\u3057\u3066<\/p>\n
\\begin{eqnarray}
\nds^2 &=& -dt^2 + t^2 \\left(\\frac{dr^2}{1 + r^2} + r^2 d\\Omega^2 \\right) \\\\
\n&=& – \\left(1 + r^2\\right) \\left(d\\tau – \\frac{r}{\\sqrt{1 + r^2}} dR\\right)^2 + \\left(1 + r^2\\right) \\left( dR – \\frac{r}{\\sqrt{1 + r^2}} d\\tau\\right)^2 + R^2 d\\Omega^2 \\\\
\n&=&-d\\tau^2 +dR^2 + R^2 d\\Omega^2
\n\\end{eqnarray}<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[20],"tags":[],"class_list":["post-2950","post","type-post","status-publish","format-standard","hentry","category-rel-cosmo","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\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