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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fluid solution ： ウィキペディア英語版 Fluid solution In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid. In astrophysics, fluid solutions are often employed as stellar models. (It might help to think of a perfect gas as a special case of a perfect fluid.) In cosmology, fluid solutions are often used as cosmological models. ==Mathematical definition== The stress–energy tensor of a relativistic fluid can be written in the form :$T^\; =\; \backslash mu\; \backslash ,\; u^a\; \backslash ,\; u^b\; +\; p\; \backslash ,\; h^\; +\; \backslash left(\; u^a\; \backslash ,\; q^b\; +\; q^a\; \backslash ,\; u^b\; \backslash right)\; +\; \backslash pi^$ Here * the world lines of the fluid elements are the integral curves of the velocity vector $u^a$, * the projection tensor $h\_\; =\; g\_\; +\; u\_a\; \backslash ,\; u\_b$ projects other tensors onto hyperplane elements orthogonal to $u^a$, * the matter density is given by the scalar function $\backslash mu$, * the pressure is given by the scalar function $p$, * the heat flux vector is given by $q^a$, * the viscous shear tensor is given by $\backslash pi^$. The heat flux vector and viscous shear tensor are ''transverse'' to the world lines, in the sense that :$q\_a\; \backslash ,\; u^a\; =\; 0,\; \backslash ;\; \backslash ;\; \backslash pi\_\; \backslash ,\; u^b\; =\; 0$ This means that they are effectively three-dimensional quantities, and since the viscous stress tensor is symmetric and traceless, they have respectively 3 and 5 linearly independent components. Together with the density and pressure, this makes a total of 10 linearly independent components, which is the number of linearly independent components in a four-dimensional symmetric rank two tensor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fluid solution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.