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The basic and fundamental aspects of General Relativity are in generalanalysed in mathematical level of coordinate basis or holonomic frame byseveral authors in the literature. However, for many purposes it is moreconvenient to use a general basis, often called in four dimensions, a tetrad orvierbein, very useful in a local frame with orthonormal basis orpseudo-orthonormal basis. This text presents an introduction to non-coordinatebasis and the two Cartan's structure equations that are mathematical implementsin Riemannian geometry that facilitate the calculation of curvature tensors.The purpose of this text is to approach the language and the notation of tetradfield or vierbein with conceptual and calculational details.

Non-coordinates basis in General Relativity and Cartan's structure equations