{"id":3985,"date":"2022-10-07T10:51:11","date_gmt":"2022-10-07T01:51:11","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3985"},"modified":"2022-10-11T14:13:40","modified_gmt":"2022-10-11T05:13:40","slug":"read_sec3-pdf-%e3%81%ae-35-%e5%bc%8f%e3%81%ae%e4%bb%b6","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3985\/","title":{"rendered":"read_sec3.pdf \u306e (36) \u5f0f\u306e\u4ef6"},"content":{"rendered":"<p>\u671d\u6c38\u541b\u3078\u306e\u79c1\u4fe1\u3002<\/p>\n<p style=\"padding-left: 40px;\">\u307e\u305a, (36)\u5f0f\u306b\u3064\u3044\u3066\u306a\u306e\u3067\u3059\u304c\u3053\u306e\u5f0f\u306b\u306f2H\\Phi\u306f\u5165\u3089\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b?<\/p>\n<p>\u3068\u3044\u3046\u8cea\u554f\u3078\u306e\u56de\u7b54\uff1a<!--more--><\/p>\n<p>10\/06 \u9001\u4ed8\u306e\u79c1\u306e read_sec3.pdf \u306e (35), (36) \u306f<br \/>\n\\begin{eqnarray}<br \/>\n\\dot{\\color{red}{\\varDelta_m}} + \\frac{1}{a^2}\\nabla^2 {\\color{blue}{V}} &amp;=&amp; 0\\tag{$\\color{red}{35}$}\\\\<br \/>\n\\dot{{\\color{blue}{V}}} + \\varPhi&amp;=&amp; 0\\tag{$\\color{red}{36}$}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3060\u3051\u3069\uff0c\u3053\u308c\u306e\u3053\u3068\uff1f<\/p>\n<p>\u3053\u308c\u3089\u304c\u6b63\u3057\u3044\u3053\u3068\u306f\uff0c\u3042\u306a\u305f\u304c\u9001\u3063\u3066\u304f\u308c\u305f 9\/14 \u306e re_paper2.pdf<\/p>\n<p>\\begin{align}<br \/>\n\\frac{\\dot{a}}{a}\\Phi_{|i} &#8211; \\dot{\\Psi}_{|i} &amp;= -4\\pi G\\bar{\\rho}_ma^2V_i\u00a0 \\tag{29}\\\\ \\ \\\\<br \/>\n\\frac{\\dot{a}}{a}\\Phi &#8211; \\dot{\\Psi} &amp;= -4\\pi G\\bar{\\rho}_ma^2V \\tag{$\\color{green}29a$}<br \/>\n\\end{align}<\/p>\n<p>\\begin{align}<br \/>\n\\dot{\\varDelta} + V^i_{|i} + 3\\dot{\\Psi} &amp;= 0 \\tag{31}\\\\ \\ \\\\<br \/>\n\\dot{\\varDelta} + \\nabla^2 V + 3\\dot{\\Psi} &amp;= 0 \\tag{$\\color{green}31a$} \\\\ \\ \\\\<br \/>\n\\dot{V}_i + 2\\frac{\\dot{a}}{a}V_i + \\frac{\\Phi_{|i}}{a^2} &amp;= 0 \\tag{32}\\\\ \\ \\\\<br \/>\n(a^2 V)^{.} + {\\Phi} &amp;= 0 \\tag{$\\color{green}32a$}<br \/>\n\\end{align}<\/p>\n<p>\\begin{gather}<br \/>\n\\mathcal{D} \\equiv \\varDelta &#8211; 3a^2HV \\tag{33}<br \/>\n\\end{gather}<\/p>\n<p>\u304c\u6b63\u3057\u3044\u3068\u3059\u308c\u3070\u793a\u305b\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\uff0c\u3042\u306a\u305f\u306e\u5909\u6570\u3068\u79c1\u306e\u5909\u6570\u306e\u95a2\u4fc2\u306f<\/p>\n<p>$$ {\\color{blue}{V}} = a^2 V, \\quad {\\color{red}{\\varDelta_m}} = \\mathcal{D}$$<\/p>\n<p>\u3042\u306a\u305f\u306e (33) \u3092 (31a) \u3078\u4ee3\u5165\u3057\u3066<\/p>\n<p>\\begin{align}<br \/>\n\\dot{\\varDelta} + \\nabla^2 V + 3\\dot{\\Psi}\u00a0 &amp;= \\left(\\mathcal{D} + 3a^2HV \\right)^{.}\u00a0 + \\nabla^2 V + 3\\dot{\\Psi}\u00a0 \\\\<br \/>\n&amp;= \\dot{\\mathcal{D}} + \\nabla^2 V\u00a0 \\\\<br \/>\n&amp;\\quad + 3 \\left\\{\\dot{H} a^2 V + H (a^2 V)^{\\cdot} + \\dot{\\Psi} \\right\\} \\\\<br \/>\n&amp;= \\dot{\\mathcal{D}} + \\nabla^2 V\u00a0 \\\\<br \/>\n&amp;\\quad + 3 \\left\\{- 4 \\pi G \\bar{\\rho}_m a^2 V + H (-\\Phi) + \\dot{\\Psi} \\right\\} \\\\<br \/>\n&amp;= \\dot{ {\\color{red}{\\varDelta_m}}} + \\nabla^2 \\frac{1}{a^2}{\\color{blue}{V}} = 0 \\tag{$\\color{red}{35}$}<br \/>\n\\end{align}<\/p>\n<p>\u6700\u5f8c\u306e\u4e2d\u62ec\u5f27\u306e\u4e2d\u8eab\u306f (29a) \u304b\u3089\u30bc\u30ed\u3002<\/p>\n<p>($\\color{red}{36}$) \u306f (32a) \u305d\u306e\u3082\u306e\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u671d\u6c38\u541b\u3078\u306e\u79c1\u4fe1\u3002<\/p>\n<p style=\"padding-left: 40px;\">\u307e\u305a, (36)\u5f0f\u306b\u3064\u3044\u3066\u306a\u306e\u3067\u3059\u304c\u3053\u306e\u5f0f\u306b\u306f2H\\Phi\u306f\u5165\u3089\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b?<\/p>\n<p>\u3068\u3044\u3046\u8cea\u554f\u3078\u306e\u56de\u7b54\uff1a<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3985\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\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":[1],"tags":[],"class_list":["post-3985","post","type-post","status-publish","format-standard","hentry","category-memo","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u671d\u6c38\u541b\u3078\u306e\u79c1\u4fe1\u3002 \u307e\u305a, (36)\u5f0f\u306b\u3064\u3044\u3066\u306a\u306e\u3067\u3059\u304c\u3053\u306e\u5f0f\u306b\u306f2H\\Phi\u306f\u5165\u3089\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b? 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