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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 Monochromatic electromagnetic plane wave ： ウィキペディア英語版 Monochromatic electromagnetic plane wave In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from Maxwell's theory. The precise definition of the solution is quite complicated, but very instructive. Any exact solution of the Einstein field equation which models an electromagnetic field must take into account all gravitational effects of the energy of the electromagnetic field itself. If there is no matter and no non-gravitational fields present other than the electromagnetic field, this means that we must ''simultaneously'' solve the Einstein field equation and the (curved spacetime, source-free) Maxwell field equations. In Maxwell's theory of electromagnetism, one of the most important types of an electromagnetic field are those representing electromagnetic radiation. Of these, the most important examples are the electromagnetic plane waves, in which the radiation has planar wavefronts moving in a specific direction at the speed of light. Of these, the most basic are the monochromatic plane waves, in which only one frequency component is present. This is precisely the phenomenon which our solution will model in terms of general relativity. ==Definition of the solution== The metric tensor of the unique exact solution modeling a linearly polarized electromagnetic plane wave with amplitude and frequency can be written, in terms of Rosen coordinates, in the form : where $\backslash xi=\backslash frac$ is the first positive root of where $a=\backslash frac$. In this chart, are null coordinate vectors while are spacelike coordinate vectors. Here, the ''Mathieu cosine'' is an even function which solves the ''Mathieu equation'' and also takes the value . Despite the name, this function is ''not'' periodic, and it cannot be written in terms of sinusoidal or even hypergeometric functions. (See Mathieu function for more about the Mathieu cosine function.) In our expression for the metric, note that are null vector fields. Therefore is a timelike vector field, while are spacelike vector fields. To define the electromagnetic field, we may take the electromagnetic four-vector potential :$\backslash vec=\backslash frac,\; \backslash frac,\; \backslash omega\; u\; \backslash right)\; \backslash ,\; \backslash sin(\backslash omega\; u)\; \backslash ,\; du\; \},\; \backslash frac,\; \backslash omega\; u\; \backslash right)\}\; \backslash ;\; \backslash partial\_x$ We now have the complete specification of a mathematical model formulated in general relativity. 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「Monochromatic electromagnetic plane wave」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.