The tetrad formalism is a transformed coordinate approach to General Relativity General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a geometric property of space and time, or spacetime.
In the tetrad formalism, a tetrad basis is chosen -- a set of four independent vector fields that together span the 4D vector space at each point in spacetime. All tensors of the theory are then expressed in this vector basis, by projecting them against members of the tetrad. For example, the spacetime metric itself can be transformed from a fixed coordinate basis to the tetrad basis:
The advantage of the tetrad formalism over the standard coordinate-based approach to GR lies in the ability to choose the tetrad basis to reflect important physical aspects of the spacetime.
Popular tetrad bases include orthonormal tetrads and null tetrads. The latter are used frequently in problems dealing with radiation, and are the basis of the Newman-Penrose formalism The Newman-Penrose Formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for General Relativity. Their notation is an effort to treat General Relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR.
Categories: Relativity The theory of relativity encompasses Einstein's theories of special and general relativity | Mathematical notation
