{"id":503,"date":"2023-01-03T10:47:22","date_gmt":"2023-01-03T01:47:22","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=503"},"modified":"2026-01-10T13:38:31","modified_gmt":"2026-01-10T04:38:31","slug":"post-503","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=503","title":{"rendered":"\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u3092\u6c42\u3081\u308b"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/daba-no-heya.com\/?p=503\/#%E5%B0%8E%E5%85%A5\" >\u5c0e\u5165<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/daba-no-heya.com\/?p=503\/#%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E3%83%BB%E9%81%8B%E5%8B%95%E9%87%8F%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB\" >\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/daba-no-heya.com\/?p=503\/#%E3%83%AA%E3%83%83%E3%83%81%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B\" >\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb\u3092\u8a08\u7b97\u3059\u308b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/daba-no-heya.com\/?p=503\/#%E4%BF%82%E6%95%B0kappa%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B\" >\u4fc2\u6570$\\kappa$\u3092\u6c42\u3081\u308b<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%B0%8E%E5%85%A5\"><\/span>\u5c0e\u5165<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u3067\u306f\u7269\u8cea\u5bc6\u5ea6$\\rho$\u304c\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$\\phi$\u3092\u4f5c\u308b\u3068\u8003\u3048\u307e\u3059\u3002<br>\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$\\phi$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\nabla^2\\phi=4\\pi G\\rho $$<\/p>\n\n\n\n<p>$G$\u306f\u91cd\u529b\u5b9a\u6570\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u304c\u30cb\u30e5\u30fc\u30c8\u30f3\u7684\u6975\u9650\u306b\u304a\u3044\u3066\u3053\u306e\u5f0f\u3092\u518d\u73fe\u3059\u308b\u3088\u3046\u306b\u3057\u305f\u3044\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E3%83%BB%E9%81%8B%E5%8B%95%E9%87%8F%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB\"><\/span>\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4ee5\u524d\u306e\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u305f\u3068\u304a\u308a\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u306f$T^{\\mu\\nu}=\\rho c^2u^{\\mu}u^{\\nu}$\u3068\u8868\u3055\u308c\u307e\u3059\u3002<br>4\u5143\u901f\u5ea6\u306e\u6642\u9593\u6210\u5206\u306f$u^t=\\gamma$\u3001\u7a7a\u9593\u6210\u5206\u306f$u^i=\\gamma\\frac{v^i}{c}$\u3068\u5b9a\u7fa9\u3057\u305f\u306e\u3067\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u8fd1\u4f3c($\\frac{v}{c}\\approx 0$)\u3067\u306f$u^t=1$\u3001$u^i=0$\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3057\u305f\u304c\u3063\u3066\u3001$T^{00}=\\rho c^2$\u4ee5\u5916\u306e\u6210\u5206\u306f\u3059\u3079\u30660\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%AA%E3%83%83%E3%83%81%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%82%92%E8%A8%88%E7%AE%97%E3%81%99%E3%82%8B\"><\/span>\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb\u3092\u8a08\u7b97\u3059\u308b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30ea\u30c3\u30c1\u30c6\u30f3\u30bd\u30eb$R_{\\mu\\nu}$\u3092\u8a08\u7b97\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} &amp;R_{\\mu\\nu}=g^{\\rho\\sigma}R_{\\mu\\rho\\nu\\sigma} \\\\ &amp;R_{\\mu\\rho\\nu\\sigma}=R_{\\mu\\rho\\nu}^{\\quad\\sigma&#8217;}g_{\\sigma&#8217;\\sigma} \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$\nR_{\\mu\\nu}=g^{\\rho\\sigma}R_{\\mu\\rho\\nu}^{\\quad\\sigma&#8217;}g_{\\sigma&#8217;\\sigma}=R_{\\mu\\rho\\nu}^{\\quad\\rho}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\nR_{\\mu\\rho\\nu}^{\\quad\\rho}=\\frac{\\partial \\Gamma^{\\rho}_{\\mu\\nu}}{\\partial x^{\\rho}}-\\frac{\\partial \\Gamma^{\\rho}_{\\rho\\nu}}{\\partial x^{\\mu}}+\\Gamma^{\\alpha}_{\\mu\\nu}\\Gamma^{\\rho}_{\\alpha\\rho}-\\Gamma^{\\alpha}_{\\rho\\nu}\\Gamma^{\\rho}_{\\alpha\\mu}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308b\u306e\u3067\u3001\u307e\u305a\u306f\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7\u3092\u8a08\u7b97\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} \\Gamma^{\\rho}_{\\mu\\nu}&amp;=\\frac{1}{2}g^{\\rho\\sigma}(\\frac{\\partial g_{\\nu\\sigma}}{\\partial x^{\\mu}}+\\frac{\\partial g_{\\mu\\sigma}}{\\partial x^{\\nu}}-\\frac{\\partial g_{\\mu\\nu}}{\\partial x^{\\sigma}}) \\\\ \\Gamma^{\\rho}_{\\rho\\nu}&amp;=\\frac{1}{2}g^{\\rho\\sigma}(\\frac{\\partial g_{\\nu\\sigma}}{\\partial x^{\\rho}}+\\frac{\\partial g_{\\rho\\sigma}}{\\partial x^{\\nu}}-\\frac{\\partial g_{\\rho\\nu}}{\\partial x^{\\sigma}}) \\end{aligned} \\right. $$<\/p>\n\n\n\n<p>\u6642\u7a7a\u306e\u6b6a\u307f\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u306f\u8a08\u91cf$g_{\\mu\\nu}$\u3092\u5e73\u5766\u8a08\u91cf$\\eta_{\\mu\\nu}$\u3067\u8fd1\u4f3c\u3067\u304d\u308b\u306e\u3067\u3001\u5fae\u5c0f\u91cf$h_{\\mu\\nu}$\u3092\u7528\u3044\u3066\u3001$g_{\\mu\\nu}=\\eta_{\\mu\\nu}+h_{\\mu\\nu}$\u3068\u8868\u3057\u307e\u3059\u3002<br>\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7\u306e\u5f0f\u306b$g_{\\mu\\nu}=\\eta_{\\mu\\nu}+h_{\\mu\\nu}$\u3092\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    \\Gamma^{\\rho}_{\\mu\\nu}&amp;=\\frac{1}{2}(\\eta^{\\rho\\sigma}+h^{\\rho\\sigma}) \\\\\n    &amp;\\qquad (\\frac{\\partial(\\eta_{\\nu\\sigma}+h_{\\nu\\sigma})}{\\partial x^{\\mu}}+\\frac{\\partial(\\eta_{\\mu\\sigma}+h_{\\mu\\sigma})}{\\partial x^{\\nu}}-\\frac{\\partial(\\eta_{\\mu\\nu}+h_{\\mu\\nu})}{\\partial x^{\\sigma}}) \\\\\n    &amp;=\\frac{1}{2}(\\eta^{\\rho\\sigma}+h^{\\rho\\sigma})(\\frac{\\partial h_{\\nu\\sigma}}{\\partial x^{\\mu}}+\\frac{\\partial h_{\\mu\\sigma}}{\\partial x^{\\nu}}-\\frac{\\partial h_{\\mu\\nu}}{\\partial x^{\\sigma}})\n\\end{align*}\n$$<\/p>\n\n\n\n<p>\u5b9a\u6570\u3067\u3042\u308b$\\eta_{\\mu\\nu}$\u306e\u5fae\u5206\u306f\u6d88\u3048\u3066\u3001$h_{\\mu\\nu}$\u306e\u5fae\u5206\u3060\u3051\u304c\u6b8b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e8c\u3064\u76ee\u306e\u62ec\u5f27\u306e\u4e2d\u306f$h_{\\mu\\nu}$\u306e\u5fae\u5206\u3067\u3042\u308a\u3001\u5fae\u5c0f\u91cf\u3067\u3059\u3002<br>\u305d\u308c\u306b$h_{\\mu\\nu}$\u3092\u304b\u3051\u305f\u3082\u306e\u306f2\u6b21\u306e\u5fae\u5c0f\u91cf\u306b\u306a\u308b\u306e\u3067\u3001\u6d88\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\n\\Gamma^{\\rho}_{\\mu\\nu}\\approx\\frac{1}{2}\\eta^{\\rho\\sigma}(\\frac{\\partial h_{\\nu\\sigma}}{\\partial x^{\\mu}}+\\frac{\\partial h_{\\mu\\sigma}}{\\partial x^{\\nu}}-\\frac{\\partial h_{\\mu\\nu}}{\\partial x^{\\sigma}})\n$$<\/p>\n\n\n\n<p>\u540c\u69d8\u306b\u3057\u3066\u3001$\\Gamma^{\\rho}_{\\rho\\nu}$\u306f<\/p>\n\n\n\n<p>$$\n\\Gamma^{\\rho}_{\\rho\\nu}\\approx\\frac{1}{2}\\eta^{\\rho\\sigma}(\\frac{\\partial h_{\\nu\\sigma}}{\\partial x^{\\rho}}+\\frac{\\partial h_{\\rho\\sigma}}{\\partial x^{\\nu}}-\\frac{\\partial h_{\\rho\\nu}}{\\partial x^{\\sigma}})\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$R_{\\mu\\rho\\nu}^{\\quad\\rho}$\u306e\u5f0f\u306b\u51fa\u3066\u304f\u308b\u30af\u30ea\u30b9\u30c8\u30c3\u30d5\u30a7\u30eb\u8a18\u53f7\u306e\u7a4d\u306f2\u6b21\u306e\u5fae\u5c0f\u91cf\u306b\u306a\u308b\u306e\u3067\u6d88\u3057\u3066\u3001<\/p>\n\n\n\n<p>$$\nR_{\\mu\\rho\\nu}^{\\quad\\rho}\\approx \\frac{\\partial \\Gamma^{\\rho}_{\\mu\\nu}}{\\partial x^{\\rho}}-\\frac{\\partial \\Gamma^{\\rho}_{\\rho\\nu}}{\\partial x^{\\mu}}\n$$<\/p>\n\n\n\n<p>\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    R_{\\mu\\nu}&amp;=R_{\\mu\\rho\\nu}^{\\quad\\rho} \\\\\n    &amp;\\approx \\frac{\\partial \\Gamma^{\\rho}_{\\mu\\nu}}{\\partial x^{\\rho}}-\\frac{\\partial \\Gamma^{\\rho}_{\\rho\\nu}}{\\partial x^{\\mu}} \\\\\n    &amp;=\\frac{1}{2}\\eta^{\\rho\\sigma}(\\frac{\\partial^2 h_{\\nu\\sigma}}{\\partial x^{\\rho}\\partial x^{\\mu}}+\\frac{\\partial^2 h_{\\mu\\sigma}}{\\partial x^{\\rho}\\partial x^{\\nu}}-\\frac{\\partial^2 h_{\\mu\\nu}}{\\partial x^{\\rho}\\partial x^{\\sigma}} \\\\\n    &amp;\\qquad -\\frac{\\partial^2 h_{\\nu\\sigma}}{\\partial x^{\\mu}\\partial x^{\\rho}}-\\frac{\\partial^2 h_{\\rho\\sigma}}{\\partial x^{\\mu}\\partial x^{\\nu}}+\\frac{\\partial^2 h_{\\rho\\nu}}{\\partial x^{\\mu}\\partial x^{\\sigma}}) \\\\\n    &amp;=\\frac{1}{2}\\eta^{\\rho\\sigma}(\\frac{\\partial^2 h_{\\mu\\sigma}}{\\partial x^{\\rho}\\partial x^{\\nu}}-\\frac{\\partial^2 h_{\\mu\\nu}}{\\partial x^{\\rho}\\partial x^{\\sigma}}-\\frac{\\partial^2 h_{\\rho\\sigma}}{\\partial x^{\\mu}\\partial x^{\\nu}}+\\frac{\\partial^2 h_{\\rho\\nu}}{\\partial x^{\\mu}\\partial x^{\\sigma}})\n\\end{align*}\n$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%BF%82%E6%95%B0kappa%E3%82%92%E6%B1%82%E3%82%81%E3%82%8B\"><\/span>\u4fc2\u6570$\\kappa$\u3092\u6c42\u3081\u308b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4ee5\u524d\u306e\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u305f\u3068\u304a\u308a\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u8fd1\u4f3c\u3067\u306f$h_{00}=-\\frac{2}{c^2}\\phi$\u3068\u306a\u308b\u306e\u3067\u3001\u3053\u3053\u3067\u306f$h_{00}$\u306e\u632f\u308b\u821e\u3044\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<br>$R_{00}$\u306b\u6ce8\u76ee\u3059\u308b\u3068$h_{00}$\u304c\u51fa\u3066\u304f\u308b\u9805\u4ee5\u5916\u3092\u6d88\u305b\u308b\u306e\u3067\u3001$R_{00}$\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    R_{00}&amp;\\approx \\frac{1}{2}\\eta^{\\rho\\sigma}(\\frac{\\partial^2 h_{0\\sigma}}{\\partial x^{\\rho}\\partial x^0}-\\frac{\\partial^2 h_{00}}{\\partial x^{\\rho}\\partial x^{\\sigma}}-\\frac{\\partial^2 h_{\\rho\\sigma}}{\\partial x^0\\partial x^0}+\\frac{\\partial^2 h_{\\rho 0}}{\\partial x^0\\partial x^{\\sigma}}) \\\\\n    &amp;=\\frac{1}{2}\\eta^{\\rho\\sigma}(-\\frac{\\partial^2 h_{00}}{\\partial x^{\\rho}\\partial x^{\\sigma}}) \\\\\n    &amp;=-\\frac{1}{2}\\eta^{\\rho\\sigma}\\partial_{\\rho}\\partial_{\\sigma}h_{00} \\\\\n    &amp;=-\\frac{1}{2}(-\\partial_0^2+\\partial_i\\partial^i)h_{00} \\\\\n    &amp;=-\\frac{1}{2}\\partial_i\\partial^ih_{00} \\\\\n    &amp;=-\\frac{1}{2}\\nabla^2h_{00}\n\\end{align*}\n$$<\/p>\n\n\n\n<p>\u7ba1\u7406\u4eba\u306f\u4e00\u884c\u76ee\u304b\u3089\u4e8c\u884c\u76ee\u3078\u306e\u5f0f\u5909\u5f62\u304c\u306a\u305c\u305d\u3046\u306a\u308b\u306e\u304b\u7406\u89e3\u3067\u304d\u306a\u304f\u3066\u3001\u4e09\u65e5\u304f\u3089\u3044\u60a9\u3093\u3067\u3044\u307e\u3057\u305f\u3002<br>\u81ea\u5206\u306f\u3059\u3063\u304b\u308a\u5fd8\u308c\u3066\u3044\u305f\u306e\u3067\u3059\u304c\u3001\u4eca\u8003\u3048\u3066\u3044\u308b\u306e\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u8fd1\u4f3c\u3067\u3059\u3002<br>\u30cb\u30e5\u30fc\u30c8\u30f3\u8fd1\u4f3c\u3067\u306f\u91cd\u529b\u5834\u306f\u6642\u9593\u7684\u306b\u5909\u5316\u3057\u306a\u3044\u3068\u4eee\u5b9a\u3057\u305f\u306e\u3067\u3001$\\partial_0 g_{\\mu\\nu}=0$\u3059\u306a\u308f\u3061$\\partial_0 h_{\\mu\\nu}=0$\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\u3057\u305f\u3002<br>\u3053\u306e\u3053\u3068\u304b\u3089\u3001$\\partial_0$\u304c\u542b\u307e\u308c\u308b\u9805\u306f\u3059\u3079\u30660\u306b\u306a\u3063\u3066\u6d88\u3048\u3066\u3057\u307e\u3046\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u5909\u5f62\u3055\u308c\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$\nR_{\\mu\\nu}=\\kappa(T_{\\mu\\nu}-\\frac{1}{2}g_{\\mu\\nu}T)\n$$<\/p>\n\n\n\n<p>\u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    R_{00}&amp;=\\kappa(T_{00}-\\frac{1}{2}g_{00}g_{00}T^{00}) \\\\\n    &amp;=\\kappa(c^2\\rho-\\frac{1}{2}(\\eta_{00}+h_{00})(\\eta_{00}+h_{00})c^2\\rho) \\\\\n    &amp;=\\kappa(c^2\\rho-\\frac{1}{2}(-1+h_{00})(-1+h_{00})c^2\\rho) \\\\\n    &amp;\\approx \\kappa(c^2\\rho-\\frac{1}{2}c^2\\rho+h_{00}c^2\\rho) \\\\\n    &amp;=\\frac{1}{2}\\kappa c^2\\rho+\\kappa c^2\\rho h_{00} \\\\\n    &amp;\\approx \\frac{1}{2}\\kappa c^2\\rho\n\\end{align*}\n$$<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p>$$\n-\\frac{1}{2}\\nabla^2h_{00}=\\frac{1}{2}\\kappa c^2\\rho\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u306b$h_{00}=-\\frac{2}{c^2}\\phi$\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$\n-\\frac{1}{2}\\nabla^2(-\\frac{2}{c^2}\\phi)=\\frac{1}{2}\\kappa c^2\\rho\n$$<\/p>\n\n\n\n<p>\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$\n\\nabla^2\\phi=\\kappa\\frac{c^4\\rho}{2}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u306b\u304a\u3051\u308b\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$\\phi$\u306f$\\nabla^2\\phi=4\\pi G\\rho$\u3067\u8868\u3055\u308c\u308b\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$\n\\kappa\\frac{c^4\\rho}{2}=4\\pi G\\rho\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308c\u3070\u3088\u3055\u305d\u3046\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u3088\u308a\u3001\u4fc2\u6570$\\kappa$\u306f<\/p>\n\n\n\n<p>$$\n\\kappa=\\frac{8\\pi G}{c^4}\n$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u3001\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f<\/p>\n\n\n\n<p>$$ R_{\\mu\\nu}-\\frac{1}{2}g_{\\mu\\nu}R=\\frac{8\\pi G}{c^4}T_{\\mu\\nu} $$<\/p>\n\n\n\n<p>\u3068\u8868\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u3067\u306f\u7269\u8cea\u5bc6\u5ea6$\\rho$\u304c\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$\\phi$\u3092\u4f5c\u308b\u3068\u8003\u3048\u307e\u3059\u3002\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$\\phi$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002 $$ \\nabla^2\\phi=4\\pi G\\rho $$ $G$\u306f\u91cd\u529b\u5b9a [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-503","post","type-post","status-publish","format-standard","hentry","category-9","category-10"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=503"}],"version-history":[{"count":12,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/503\/revisions"}],"predecessor-version":[{"id":1663,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/503\/revisions\/1663"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}