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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 Electrovacuum solution ： ウィキペディア英語版 Electrovacuum solution In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass-energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) ''source-free'' Maxwell equations appropriate to the given geometry. For this reason, electrovacuums are sometimes called (source-free) Einstein-Maxwell solutions. ==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 $\backslash ,\; g\_$ (or by defining a frame field). The curvature tensor $\backslash ,\; R\_$ 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. We also need to specify an electromagnetic field by defining an electromagnetic field tensor $F\_$ on our Lorentzian manifold. These two tensors are required to satisfy two following conditions # The electromagnetic field tensor must satisfy the ''source-free'' curved spacetime Maxwell field equations $\backslash ,\; F\_\; +\; F\_\; +\; F\_\; =\; 0$ and $=\; 0$ # The Einstein tensor must match the electromagnetic stress-energy tensor, $G^=\; 2\; \backslash ,\; \backslash left(\; F^-\backslash fracg^\; \backslash ,\; F^\; \backslash ,\; F\_\; \backslash right\; )$. The first Maxwell equation is satisfied automatically if we define the field tensor in terms of an electromagnetic potential vector $\backslash vec$. In terms of the dual covector (or potential one-form) and the electromagnetic two-form, we can do this by setting $F\; =\; dA$. Then we need only ensure that the divergences vanish (i.e. that the second Maxwell equation is satisfied for a ''source-free'' field) and that the electromagnetic stress-energy matches the Einstein 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「Electrovacuum 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.