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The tetrad formalism is an approach to general relativity that replaces the choice of a coordinate basis by the less restrictive choice of a local basis for the tangent bundle, i.e. a locally defined set of four linearly independent vector fields called a tetrad. In the tetrad formalism all tensors are represented in terms of a chosen basis. (When generalised to other than four dimensions this approach is given other names, see Cartan formalism.) As a formalism rather than a theory, it does not make different predictions but does allow the relevant equations to be expressed differently. The advantage of the tetrad formalism over the standard coordinate-based approach to general relativity lies in the ability to choose the tetrad basis to reflect important physical aspects of the spacetime. The abstract index notation denotes tensors as if they were represented by their coefficients with respect to a fixed local tetrad. Compared to a completely coordinate free notation, which is often conceptually clearer, it allows an easy and computationally explicit way to denote contractions. ==Mathematical formulation== In the tetrad formalism, a tetrad basis is chosen: a set of four independent vector fields that together span the 4D vector tangent space at each point in spacetime. Dually, a tetrad determines (and is determined by) a dual co-tetrad—a set of four independent covectors (1-forms) such that : where is the Kronecker delta. A tetrad is usually specified by its coefficients with respect to a coordinate basis, despite the fact that the choice of a tetrad does not actually require the additional choice of a set of (local) coordinates . From a mathematical point of view, the four vector fields define a section of the frame bundle i.e. a parallelization of which is equivalent to an isomorphism . Since not every manifold is parallelizable, a tetrad can generally only be chosen locally. All tensors of the theory can be expressed in the vector and covector basis, by expressing them as linear combinations of members of the (co)tetrad. For example, the spacetime metric itself can be transformed from a coordinate basis to the tetrad basis. Popular tetrad bases include orthonormal tetrads and null tetrads. Null tetrads are composed of light cone vectors, so are used frequently in problems dealing with radiation, and are the basis of the Newman–Penrose formalism and the GHP formalism. 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「tetrad formalism」の詳細全文を読む スポンサード リンク
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