翻訳と辞書 Words near each other ・ Maxwell Upson ・ Maxwell v. Dow ・ Maxwell Van Zandt Woodhull ・ Maxwell W. Strange ・ Maxwell Walters ・ Maxwell Ward, 6th Viscount Bangor ・ Maxwell Wintrobe ・ Maxwell Woodhull House ・ Maxwell Woosnam (priest) ・ Maxwell Xolani Rani ・ Maxwell's ・ Maxwell's black weaver ・ Maxwell's demon ・ Maxwell's duiker ・ Maxwell's equations ・ Maxwell's equations in curved spacetime ・ Maxwell's Executors v. Wilkinson ・ Maxwell's Maniac ・ Maxwell's Plum ・ Maxwell's Silver Hammer ・ Maxwell's theorem ・ Maxwell's thermodynamic surface ・ Maxwell's Urban Hang Suite ・ Maxwell, California ・ Maxwell, Grey County, Ontario ・ Maxwell, Hastings County, Ontario ・ Maxwell, Indiana ・ Maxwell, Iowa ・ Maxwell, Morgan County, Indiana ・ Maxwell, Nebraska Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maxwell's equations in curved spacetime ： ウィキペディア英語版 Maxwell's equations in curved spacetime In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may not be the Minkowski metric) or where one uses an arbitrary (not necessarily Cartesian) coordinate system. These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime. But because general relativity dictates that the presence of electromagnetic fields (or energy/matter in general) induce curvature in spacetime,〔http://www.springerlink.com/content/h224886u7651v774/〕 Maxwell's equations in flat spacetime should be viewed as a convenient approximation. When working in the presence of bulk matter, it is preferable to distinguish between free and bound electric charges. Without that distinction, the vacuum Maxwell's equations are called the "microscopic" Maxwell's equations. When the distinction is made, they are called the macroscopic Maxwell's equations. The electromagnetic field also admits a coordinate-independent geometric description, and Maxwell's equations expressed in terms of these geometric objects are the same in any spacetime, curved or not. Also, the same modifications are made to the equations of flat Minkowski space when using local coordinates that are not Cartesian. For example, the equations in this article can be used to write Maxwell's equations in spherical coordinates. For these reasons, it may be useful to think of Maxwell's equations in Minkowski space as a special case, rather than Maxwell's equations in curved spacetimes as a generalization. ==Summary== In general relativity, the metric, ''g''αβ, is no longer a constant (like ηαβ as in Examples of metric tensor) but can vary in space and time, and the equations of electromagnetism in a vacuum become: :$F\_\; \backslash ,\; =\; \backslash ,\; \backslash partial\_\; A\_\; \backslash ,\; -\; \backslash ,\; \backslash partial\_\; A\_\; \backslash ,$ :$\backslash mathcal^\; \backslash ,\; =\; \backslash ,\; \backslash frac\; \backslash ,\; F\_\; \backslash ,\; g^\; \backslash ,\; \backslash sqrt\; \backslash ,$ :$J^\; \backslash ,\; =\; \backslash ,\; \backslash partial\_\backslash nu\; \backslash mathcal^\; \backslash ,$ :$f\_\backslash mu\; \backslash ,\; =\; \backslash ,\; F\_\; \backslash ,\; J^\backslash nu\; \backslash ,$ where ''f''μ is the density of the Lorentz force, ''g''αβ is the reciprocal of the metric tensor ''g''αβ, and ''g'' is the determinant of the metric tensor. Notice that ''A''α and ''F''αβ are (ordinary) tensors while $\backslash mathcal^$, ''J''ν, and ''f''μ are tensor ''densities'' of weight +1. Despite the use of partial derivatives, these equations are invariant under arbitrary curvilinear coordinate transformations. Thus if one replaced the partial derivatives with covariant derivatives, the extra terms thereby introduced would cancel out. (Cf. manifest covariance#Example.) 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「Maxwell's equations in curved spacetime」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.