{"id":3189,"date":"2022-07-08T13:46:08","date_gmt":"2022-07-08T04:46:08","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3189"},"modified":"2024-03-11T10:55:00","modified_gmt":"2024-03-11T01:55:00","slug":"%e3%82%ab%e3%83%86%e3%83%8a%e3%83%aa%e3%83%bc%e6%9b%b2%e7%b7%9a","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3189\/","title":{"rendered":"\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda"},"content":{"rendered":"<p>\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306b\u4e00\u69d8\u306a\u8cea\u91cf\u7dda\u5bc6\u5ea6\u306e\u30ed\u30fc\u30d7\u3092\u4e21\u7aef\u3092\u56fa\u5b9a\u3057\u3066\u5782\u3089\u3057\u305f\u3068\u304d\u306b\u3067\u304d\u308b\u66f2\u7dda\u304c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda<\/strong><\/span>\u3002<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u61f8\u5782\u66f2\u7dda<\/strong><\/span>\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u61f8\u5782\u7dda<\/strong><\/span>\u3068\u3082\u3002<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6603\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-640x308.png\" alt=\"\" width=\"640\" height=\"308\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-640x308.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-300x144.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-1536x739.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-2048x986.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/IMG_6965-750x361.png 750w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/>\u4ee5\u4e0b\u3082\u53c2\u7167\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3240\/\">\u5909\u5206\u539f\u7406\u304b\u3089\u6c42\u3081\u308b\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda<\/a><\/li>\n<\/ul>\n<hr \/>\n<p><!--more--><\/p>\n<p>\u91cd\u529b\u52a0\u901f\u5ea6 $g$ \u3067\u8868\u3055\u308c\u308b\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306b\uff0c\u4e21\u7aef\u3092\u56fa\u5b9a\u3057\u3066\u5782\u3089\u3057\u305f\u4e00\u69d8\u306a\u8cea\u91cf\u7dda\u5bc6\u5ea6 $\\rho$ \u306e\u30ed\u30fc\u30d7\uff08\u30ef\u30a4\u30e4\u30fc\uff0c\u96fb\u7dda\u7b49\u306a\u3093\u3067\u3082\u3088\u3044\uff09\u3092\u8003\u3048\u308b\u3002<\/p>\n<p>\u6c34\u5e73\u65b9\u5411\u3092 $x$\uff0c\u5782\u76f4\u65b9\u5411\u3092 $y$\uff0c\u30ed\u30fc\u30d7\u4e0a\u306e\u4f4d\u7f6e\u3092 $(x, y)$ \u3068\u3057\u3066\uff0c\u307e\u305a\uff0c$y$ \u306f\u4ee5\u4e0b\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f<\/p>\n<p>$$\\frac{d^2 y}{dx^2} = a \\sqrt{1 + \\left( \\frac{dy}{dx} \\right)^2}$$<\/p>\n<p>\u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u793a\u3059\u3002\u3053\u3053\u3067<\/p>\n<p>$$a \\equiv \\frac{\\rho g}{T_0}$$\u3067\u3042\u308a\uff0c$T_0$ \u306f $\\frac{dy}{dx} = 0$ \u306e\u70b9\u306b\u304a\u3051\u308b\u30ed\u30fc\u30d7\u306e\u5f35\u529b\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u306e\u65b9\u7a0b\u5f0f\u306b\u306f\u540d\u524d\u304c\u306a\u3044\u3088\u3046\u3067\u3059\u304c\uff0c\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u3092\u3042\u3089\u308f\u3059\u65b9\u7a0b\u5f0f\u3068\u3044\u3046\u3053\u3068\u3067\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ab\u30c6\u30ca\u30ea\u30fc\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3068\u3053\u3053\u3067\u306f\u547c\u3076\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n<p>\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u306f <a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%AB%E3%83%86%E3%83%8A%E3%83%AA%E3%83%BC%E6%9B%B2%E7%B7%9A\" target=\"_blank\" rel=\"noopener\">Wikipedia<\/a> \u3092\u306f\u3058\u3081\u591a\u304f\u306eWeb\u30da\u30fc\u30b8\u306b\u305d\u306e\u8aac\u660e\u304c\u3055\u308c\u3066\u3044\u308b\u307b\u3069\u306b\u6709\u540d\u3067\u3042\u308b\u304c\uff0c\u4ed6\u4eba\u306e\u8a71\u3092\u805e\u3044\u3066\u3082\u8aad\u3093\u3067\u3082\u306a\u304b\u306a\u304b\u7406\u89e3\u3067\u304d\u306a\u3044\u81ea\u5206\u81ea\u8eab\u306e\u305f\u3081\u306b\uff0c\u81ea\u5206\u304c\u7d0d\u5f97\u3067\u304d\u308b\u3088\u3046\u306b\uff0c\u3082\u3046\u5c11\u3057\u304b\u307f\u304f\u3060\u3044\u3066\u8aac\u660e\u3057\u3066\u307f\u308b\u3002<\/p>\n<h3>\u30ab\u30c6\u30ca\u30ea\u30fc\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa<\/h3>\n<h4>\u30ed\u30fc\u30d7\u7d20\u7247\u306b\u304b\u304b\u308b\u529b\u306e\u3064\u308a\u3042\u3044<\/h4>\n<p>\u307e\u305a\uff0c\u30ed\u30fc\u30d7\u4e0a\u306e\u70b9 $P(x, y(x))$ \u304b\u3089 $x&#8217; \\equiv x + dx$ \u3068\u3057\u3066\u70b9 $Q(x&#8217;, y(x&#8217;))$ \u307e\u3067\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5fae\u5c0f\u306a\u30ed\u30fc\u30d7\u7d20\u7247<\/strong><\/span>\u3092\u8003\u3048\u308b\u3002\uff08\u56f3\u306e<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u8d64\u3044\u90e8\u5206<\/strong><\/span>\u3002\u3053\u306e\u5fae\u5c0f\u7d20\u7247\u306b\u50cd\u304f\u529b\u306e\u3064\u308a\u3042\u3044\u3092\u8003\u3048\u308b\u3068\u3053\u308d\u304c\u79c1\u306e\u3061\u3087\u3063\u3068\u3057\u305f\u3053\u3060\u308f\u308a\u3002\uff09<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3381\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-640x546.png\" alt=\"\" width=\"480\" height=\"410\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-640x546.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-300x256.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-1536x1311.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-2048x1748.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/catenary-fig-750x640.png 750w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>\u30ed\u30fc\u30d7\u306e\u9759\u6b62\u5f62\u72b6 $y(x)$ \u306f\uff0c\u3053\u306e\u30ed\u30fc\u30d7\u7d20\u7247\u306e\u4e00\u65b9\u306e\u7aef\u306b\u304b\u304b\u308b\u5f35\u529b $T(x)$ \u3068\u4ed6\u65b9\u306e\u7aef\u306b\u304b\u304b\u308b\u5f35\u529b $T(x&#8217;)$ \u304a\u3088\u3073\u30ed\u30fc\u30d7\u7d20\u7247\u306e\u8cea\u91cf\u3092 $m$ \u3068\u3057\u305f\u3068\u304d\u306e\u91cd\u529b $mg$ \u3068\u306e\u3064\u308a\u3042\u3044\u304b\u3089\u6c42\u3081\u3089\u308c\u308b\u3002<\/p>\n<p>\u30ed\u30fc\u30d7\u7d20\u7247\u306e\u50be\u304d\u89d2 $\\varphi(x)$ \u306f<\/p>\n<p>$$\\tan \\varphi(x) = \\frac{dy}{dx} = y'(x)$$<\/p>\n<p>\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002<\/p>\n<h5>\u6c34\u5e73\u65b9\u5411\u306e\u529b\u306e\u3064\u308a\u3042\u3044<\/h5>\n<p>\u3053\u306e\u30ed\u30fc\u30d7\u7d20\u7247\u306b\u306f\u305f\u3089\u304f\u529b\u306e\u6c34\u5e73\u65b9\u5411\u306e\u3064\u308a\u3042\u3044\u306e\u5f0f\u306f<\/p>\n<p>$$ T(x) \\cos\\varphi(x) = T(x&#8217;) \\cos\\varphi(x&#8217;) \\tag{1}$$<\/p>\n<p>\u3053\u308c\u304b\u3089\u76f4\u3061\u306b<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d}{dx} \\left( T(x) \\cos\\varphi(x) \\right) &amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ T(x) \\cos\\varphi(x) &amp;=&amp; \\mbox{const.} \\\\<br \/>\n&amp;\\equiv&amp; T_0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u3053\u3067 $T_0$ \u306f $\\varphi = 0$ \u3064\u307e\u308a $\\frac{dy}{dx} = 0$ \u306e\u70b9\u3067\u306e\u30ed\u30fc\u30d7\u306e\u5f35\u529b\u3067\u3042\u308b\u3002<\/p>\n<h5>\u5782\u76f4\u65b9\u5411\u306e\u529b\u306e\u3064\u308a\u3042\u3044<\/h5>\n<p>\u5782\u76f4\u65b9\u5411\u306e\u529b\u306e\u3064\u308a\u3042\u3044\u306e\u5f0f\u306f<\/p>\n<p>$$ T(x) \\sin\\varphi(x) + mg = T(x&#8217;) \\sin\\varphi(x&#8217;) \\tag{2}$$<\/p>\n<p>\u30ed\u30fc\u30d7\u7d20\u7247\u306e\u8cea\u91cf $m$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nm &amp;=&amp; \\rho \\sqrt{dx^2 + dy^2} \\\\<br \/>\n&amp;=&amp; \\rho \\sqrt{1 + \\left(\\frac{dy}{dx}\\right)^2} \\ dx \\\\<br \/>\n&amp;=&amp; \\rho \\sqrt{1 + \\tan^2 \\varphi} \\ dx \\\\<br \/>\n&amp;=&amp; \\frac{\\rho}{\\cos\\varphi(x)} \\ dx<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3067\u3042\u308b\u304b\u3089\uff0c\u3053\u308c\u3092 $(2)$ \u5f0f\u306b\u4ee3\u5165\u3057\u3066\u4e21\u8fba\u306b $\\cos\\varphi(x)$ \u3092\u304b\u3051\u308b\u3068<\/p>\n<p>$${\\color{blue}{T(x)\\cos\\varphi(x)}} \\sin\\varphi(x) + \\rho g dx = T(x&#8217;) \\sin\\varphi(x&#8217;) \\cos\\varphi(x)$$<\/p>\n<p>\u3053\u306e\u5f0f\u306e<span style=\"color: #0000ff;\">\u5de6\u8fba\u7b2c1\u9805<\/span>\u306b $(1)$ \u5f0f\u3092\u4ee3\u5165\u3057\u3066<\/p>\n<p>$${\\color{blue}{T(x&#8217;) \\cos\\varphi(x&#8217;)}}\\sin\\varphi(x) + \\rho g dx = T(x&#8217;) \\sin\\varphi(x&#8217;) \\cos\\varphi(x)$$<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\therefore\\ \\ \\rho g dx &amp;=&amp; T(x&#8217;) \\sin\\varphi(x&#8217;) \\cos\\varphi(x) &#8211; T(x&#8217;) \\cos\\varphi(x&#8217;)\\sin\\varphi(x) \\\\<br \/>\n&amp;=&amp; T(x&#8217;) \\sin(\\varphi(x&#8217;) &#8211; \\varphi(x)) \\\\<br \/>\n&amp;\\simeq&amp; \\left(T(x) + \\frac{dT}{dx} dx \\right) \\sin\\left( \\frac{d\\varphi}{dx} dx \\right) \\\\<br \/>\n&amp;\\simeq&amp;T(x) \\frac{d\\varphi}{dx} dx \\\\ \\ \\\\<br \/>\n\\therefore\\ \\ \\frac{d\\varphi}{dx} &amp;=&amp; \\frac{\\rho g}{T(x)}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u308c\u3092 $y$ \u306b\u3064\u3044\u3066\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u3059\u308b\u305f\u3081\u306b\uff0c$\\frac{dy}{dx} = \\tan\\varphi$ \u306e\u4e21\u8fba\u3092 $x$ \u3067\u5fae\u5206\u3059\u308b\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{dy}{dx} &amp;=&amp; \\tan\\varphi \\\\<br \/>\n\\frac{d^2y}{dx^2} &amp;=&amp; \\frac{d}{dx} \\tan\\varphi \\\\<br \/>\n&amp;=&amp; \\frac{1}{\\cos^2\\varphi} \\frac{d\\varphi}{dx}\\\\<br \/>\n&amp;=&amp; \\frac{1}{\\cos^2\\varphi}\\frac{\\rho g}{T(x)} \\\\<br \/>\n&amp;=&amp; \\frac{\\rho g}{T(x) \\cos\\varphi(x)} \\frac{1}{\\cos\\varphi} \\\\<br \/>\n&amp;=&amp; \\frac{\\rho g}{T_0} \\sqrt{1 + \\tan^2\\varphi}\\\\<br \/>\n&amp;=&amp; a \\sqrt{1 + \\left( \\frac{dy}{dx}\\right)^2}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u308a\uff0c\u6c42\u3081\u3089\u308c\u305f\u3002<\/p>\n<h3>\u30ab\u30c6\u30ca\u30ea\u30fc\u65b9\u7a0b\u5f0f\u306e\u89e3<\/h3>\n<p>$$\\frac{d^2 y}{dx^2} = a \\sqrt{1 + \\left( \\frac{dy}{dx} \\right)^2}$$<\/p>\n<p>$\\displaystyle \\frac{dy}{dz} = z$ \u3068\u304a\u304f\u3068\uff0c\u5909\u6570\u5206\u96e2\u3067\u304d\u3066\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e9%80%86%e5%8f%8c%e6%9b%b2%e7%b7%9a%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\" rel=\"noopener\">\u9006\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u5fae\u5206<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3092\u307f\u308c\u3070<\/p>\n<p>$$ (\\sinh^{-1} x)&#8217; =\u00a0 \\frac{1}{\\sqrt{x^2 + 1}}$$<\/p>\n<p>\u3067\u3042\u3063\u305f\u304b\u3089\uff0c\u305f\u3060\u3061\u306b<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{dz}{dx} &amp;=&amp; a \\sqrt{1 + z^2} \\\\<br \/>\n\\frac{dz}{\\sqrt{1 + z^2}} &amp;=&amp; a \\,dx \\\\<br \/>\n\\int\\frac{dz}{\\sqrt{1 + z^2}} &amp;=&amp; \\int a \\,dx \\\\<br \/>\n\\sinh^{-1} z &amp;=&amp; a x + C \\\\<br \/>\n\\therefore\\ \\ z = \\frac{dy}{dx} &amp;=&amp; \\sinh(ax + C)<br \/>\n\\end{eqnarray}<\/p>\n<p>$x = 0$ \u3067 $\\displaystyle y = h, \\ \\frac{dy}{dx} = 0$ \u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3092\u8ab2\u3059\u3068 $C = 0$\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{dy}{dx} &amp;=&amp; \\sinh(ax) \\\\<br \/>\n\\therefore\\ \\ y &amp;=&amp; \\int \\sinh(ax) \\, dx = \\frac{1}{a} \\cosh( ax ) + C<br \/>\n\\end{eqnarray}<\/p>\n<p>$x = 0$ \u3067 $y = h$ \u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3088\u308a $C = h &#8211; \\frac{1}{a}$<\/p>\n<p>$$\\therefore\\ \\ y = \\frac{1}{a} \\left( \\cosh( ax ) -1 \\right) + h$$<\/p>\n<p>\u3053\u308c\u304c\uff08\u5b9a\u6570\u90e8\u5206\u3092\u306e\u305e\u3051\u3070 $y = \\frac{1}{a} \\cosh (ax)$ \u304c\uff09\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u3067\u3042\u308b\u3002<\/p>\n<h4>\u6700\u4e0b\u70b9\u8fd1\u508d\u3067\u306e\u8fd1\u4f3c\u8868\u73fe<\/h4>\n<p>\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u306f\uff0c\u53cc\u66f2\u7dda\u95a2\u6570\u30cf\u30a4\u30d1\u30dc\u30ea\u30c3\u30af\u30fb\u30b3\u30b5\u30a4\u30f3\u3067\u3042\u3089\u308f\u3055\u308c\uff0c\u653e\u7269\u7dda\u3067\u306f\u306a\u3044\u3002<\/p>\n<p>\u305f\u3060\u3057\uff0c\u30ed\u30fc\u30d7\u306e\u8cea\u91cf\u7dda\u5bc6\u5ea6 $\\rho$ \u304c\u5c0f\u3055\u3044\u3068\u3057\u3066 $\\rho$ \u3057\u305f\u304c\u3063\u3066 $a = \\frac{\\rho g}{T_0}$ \u306e1\u6b21\u307e\u3067\u5c55\u958b\u3059\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\ny &amp;=&amp; \\frac{1}{a} \\left( \\cosh( ax ) -1 \\right) + h \\\\<br \/>\n&amp;\\simeq&amp; \\frac{1}{a} \\left( 1 + \\frac{a^2 x^2}{2} + \\cdots -1\\right) + h \\\\<br \/>\n&amp;\\simeq&amp; h + \\frac{1}{2} a x^2<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u308a\uff0c$\\rho$ \u3057\u305f\u304c\u3063\u3066 $a = \\frac{\\rho g}{T_0}$ \u304c\u5c0f\u3055\u3044\u3068\u3044\u3046\u72b6\u6cc1\uff08\u3042\u308b\u3044\u306f\u540c\u7b49\u306a\u3053\u3068\u3060\u304c\uff0c\u6700\u4e0b\u70b9 $x = 0$ \u306e\u8fd1\u508d\uff09\u3067\u306f\uff0c\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u306f\u653e\u7269\u7dda\u3068\u3057\u3066\u8fd1\u4f3c\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<h3>\u5b87\u5b99\u8ad6\u306b\u3042\u3089\u308f\u308c\u308b\u30ab\u30c6\u30ca\u30ea\u30fc<\/h3>\n<p>\u300c<a href=\"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%E5%AE%87%E5%AE%99%E8%AB%96\/%E5%AE%87%E5%AE%99%E8%AB%96%E3%83%91%E3%83%A9%E3%83%A1%E3%83%BC%E3%82%BF%E3%81%A8%E5%AE%87%E5%AE%99%E5%B9%B4%E9%BD%A2\/%E8%A3%9C%E8%B6%B3%EF%BC%9A%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B%A0%E5%AD%90%E3%81%AE%E8%A7%A3\/\" target=\"_blank\" rel=\"noopener\">\u88dc\u8db3\uff1a\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50\u306e\u89e3<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3067 $\\Omega_{\\rm m} = 0, \\ \\Omega_{\\Lambda} &gt; 1$ \uff08\u3057\u305f\u304c\u3063\u3066 $k &gt; 0$\uff09\u306e\u5834\u5408\u306b\uff0c<a href=\"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%e5%ae%87%e5%ae%99%e8%ab%96\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9a%e3%82%b9%e3%82%b1%e3%83%bc%e3%83%ab%e5%9b%a0%e5%ad%90%e3%81%ae%e8%a7%a3\/#Omega_Lambda_gt_1\" target=\"_blank\" rel=\"noopener\">\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50\u304c\u30cf\u30a4\u30d1\u30dc\u30ea\u30c3\u30af\u30fb\u30b3\u30b5\u30a4\u30f3\u3092\u4f7f\u3063\u3066\u66f8\u304b\u308c\u308b<\/a>\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u3075\u308b\u307e\u3044\u3092\u3059\u308b\u5b87\u5b99\u3092\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ab\u30c6\u30ca\u30ea\u30fc\u5b87\u5b99<\/strong><\/span>\u300d\u3068\u547c\u3093\u3067\u3044\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306b\u4e00\u69d8\u306a\u8cea\u91cf\u7dda\u5bc6\u5ea6\u306e\u30ed\u30fc\u30d7\u3092\u4e21\u7aef\u3092\u56fa\u5b9a\u3057\u3066\u5782\u3089\u3057\u305f\u3068\u304d\u306b\u3067\u304d\u308b\u66f2\u7dda\u304c\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda\u3002\u61f8\u5782\u66f2\u7dda\uff0c\u61f8\u5782\u7dda\u3068\u3082\u3002\u4ee5\u4e0b\u3082\u53c2\u7167\uff1a<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3189\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>\u5909\u5206\u539f\u7406\u304b\u3089\u6c42\u3081\u308b\u30ab\u30c6\u30ca\u30ea\u30fc\u66f2\u7dda<\/li>\n<\/ul>\n","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":[21],"tags":[],"class_list":["post-3189","post","type-post","status-publish","format-standard","hentry","category-21","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=3189"}],"version-history":[{"count":39,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3189\/revisions"}],"predecessor-version":[{"id":7974,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3189\/revisions\/7974"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=3189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=3189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=3189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}