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- Calculations in the Newman–Penrose (NP) formalism of general relativity normally begin with the construction of a complex null tetrad , where is a pair of real null vectors and is a pair of complex null vectors. These tetrad vectors respect the following normalization and metric conditions assuming the spacetime signature
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* Only after the tetrad gets constructed can one move forward to compute the directional derivatives, spin coefficients, commutators, Weyl-NP scalars , Ricci-NP scalars and Maxwell-NP scalars and other quantities in NP formalism. There are three most commonly used methods to construct a complex null tetrad: 1.
* All four tetrad vectors are nonholonomic combinations of orthonormal holonomic tetrads; 2.
* (or ) are aligned with the outgoing (or ingoing) tangent vector field of null radial geodesics, while and are constructed via the nonholonomic method; 3.
* A tetrad which is adapted to the spacetime structure from a 3+1 perspective, with its general form being assumed and tetrad functions therein to be solved. In the context below, it will be shown how these three methods work. Note: In addition to the convention employed in this article, the other one in use is . (en)
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- 16228 (xsd:nonNegativeInteger)
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- Calculations in the Newman–Penrose (NP) formalism of general relativity normally begin with the construction of a complex null tetrad , where is a pair of real null vectors and is a pair of complex null vectors. These tetrad vectors respect the following normalization and metric conditions assuming the spacetime signature
*
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* In the context below, it will be shown how these three methods work. Note: In addition to the convention employed in this article, the other one in use is . (en)
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- Construction of a complex null tetrad (en)
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