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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 Scalar field solution ： ウィキペディア英語版 Scalar field solution In general relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to the field energy and momentum of a scalar field. Such a field may or may not be ''massless'', and it may be taken to have ''minimal curvature coupling'', or some other choice, such as ''conformal coupling''. ==Mathematical definition== In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor $g\_$ (or by defining a frame field). The curvature tensor $R\_$ of this manifold and associated quantities such as the Einstein tensor $G^$, are well-defined even in the absence of any physical theory, but in general relativity they acquire a physical interpretation as geometric manifestations of the gravitational field. In addition, we must specify a scalar field by giving a function $\backslash psi$. This function is required to satisfy two following conditions: # The function must satisfy the (curved spacetime) ''source-free'' wave equation $g^\; \backslash psi\_\; =\; 0$, # The Einstein tensor must match the stress-energy tensor for the scalar field, which in the simplest case, a ''minimally coupled massless scalar field'', can be written $G^=\; 8\; \backslash pi\; \backslash left(\; \backslash psi^\; \backslash psi^\; -\; \backslash frac$ \psi_ \psi^ g^ \right) . Both conditions follow from varying the Lagrangian density for the scalar field, which in the case of a minimally coupled massless scalar field is :$L\; =\; -g^\; \backslash ,\; \backslash psi\_\; \backslash ,\; \backslash psi\_$ Here, :$\backslash frac\; =\; 0$ gives the wave equation, while :$\backslash frac\{\backslash delta\; g^\{ab\}\}\; =\; 0$ gives the Einstein equation (in the case where the field energy of the scalar field is the only source of the gravitational field). 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「Scalar field 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.