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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 Brinkmann coordinates ： ウィキペディア英語版 Brinkmann coordinates Brinkmann coordinates (named for Hans Brinkmann) are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. In terms of these coordinates, the metric tensor can be written as :$ds^2\; \backslash ,\; =\; H(u,x,y)\; du^2\; +\; 2\; du\; dv\; +\; dx^2\; +\; dy^2$ where $\backslash partial\_$, the coordinate vector field dual to the covector field $dv$, is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave. The coordinate vector field $\backslash partial\_$ can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of $H(u,x,y)$ at that event. The coordinate vector fields $\backslash partial\_,\; \backslash partial\_$ are both spacelike vector fields. Each surface $u=u\_,\; v=v\_$ can be thought of as a wavefront. In discussions of exact solutions to the Einstein field equation, many authors fail to specify the intended range of the coordinate variables $u,v,x,y$. Here we should take to allow for the possibility that the pp-wave develops a null curvature singularity. ==References== * * 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「Brinkmann coordinates」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.