\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f<\/p>\n\n\n\n
$$\nR^{\\mu\\nu}-\\frac{1}{2}g^{\\mu\\nu}R=\\kappa T^{\\mu\\nu}\n$$<\/p>\n\n\n\n
\u3068\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u524d\u56de\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
\u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc$R$\u306e\u8a08\u7b97\u306f\u8907\u96d1\u306a\u306e\u3067\u3001\u3069\u3046\u306b\u304b\u3057\u3066\u305d\u308c\u3092\u8a08\u7b97\u305b\u305a\u306b\u6e08\u3080\u65b9\u6cd5\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\u3002
\u5b9f\u306f\u3001\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3092\u5f0f\u5909\u5f62\u3059\u308b\u3053\u3068\u3067\u3001$R$\u3092\u5f0f\u304b\u3089\u306a\u304f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u4e21\u8fba\u306b$g_{\\mu\\sigma}g_{\\nu\\tau}$\u3092\u304b\u3051\u307e\u3059\u3002<\/p>\n\n\n\n
$$\n\\begin{align*}\n &g_{\\mu\\sigma}g_{\\nu\\tau}R^{\\mu\\nu}-\\frac{1}{2}g_{\\mu\\sigma}g_{\\nu\\tau}g^{\\mu\\nu}R=\\kappa g_{\\mu\\sigma}g_{\\nu\\tau}T^{\\mu\\nu} \\\\\n &\\Leftrightarrow R_{\\sigma\\tau}-\\frac{1}{2}g_{\\sigma\\tau}R=\\kappa T_{\\sigma\\tau}\n\\end{align*}\n$$<\/p>\n\n\n\n
\u3055\u3089\u306b$g^{\\sigma\\tau}$\u3092\u304b\u3051\u307e\u3059\u3002<\/p>\n\n\n\n
\\begin{align*}\n &g^{\\sigma\\tau}R_{\\sigma\\tau}-\\frac{1}{2}g^{\\sigma\\tau}g_{\\sigma\\tau}R=\\kappa g^{\\sigma\\tau}T_{\\sigma\\tau} \\\\\n &\\Leftrightarrow R^{\\sigma}_{\\;\\sigma}-\\frac{1}{2}\\delta^{\\sigma}_{\\;\\sigma}R=\\kappa T^{\\sigma}_{\\;\\sigma} \\\\\n &\\Leftrightarrow R-\\frac{1}{2}\\cdot 4R=\\kappa T \\\\\n &\\Leftrightarrow R=-\\kappa T\n\\end{align*}<\/p>\n\n\n\n
\u3053\u308c\u3092\u6700\u521d\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u6574\u7406\u3059\u308c\u3070\u3001<\/p>\n\n\n\n
$$\nR^{\\mu\\nu}=\\kappa(T^{\\mu\\nu}-\\frac{1}{2}g^{\\mu\\nu}T)\n$$<\/p>\n\n\n\n
\u3068\u306a\u308a\u307e\u3059\u3002
\u8907\u96d1\u306a$R$\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u306a\u304f\u306a\u308a\u3001\u4ee3\u308f\u308a\u306b$T=g_{\\mu\\nu}T^{\\mu\\nu}$\u3092\u8a08\u7b97\u3059\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f $$ R^{\\mu\\nu}-\\frac{1}{2}g^{\\mu\\nu}R=\\kappa T^{\\mu\\nu} $$ \u3068\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u524d\u56de\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002 \u30ea\u30c3\u30c1\u30b9\u30ab\u30e9\u30fc$R$\u306e\u8a08\u7b97\u306f\u8907\u96d1\u306a\u306e\u3067\u3001\u3069 […]<\/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-494","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\/494","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=494"}],"version-history":[{"count":4,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":794,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions\/794"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}