= Newman-Penrose formalism
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{wiki=Newman–Penrose_formalism}
The <Newman-Penrose formalism> expresses spacetime geometry in a <complex null tetrad>: two real null directions and a complex-conjugate transverse pair. Contracting the <Weyl tensor> with these vectors packages its ten real components into five complex quantities. Other contractions describe Ricci curvature and the connection in the same basis. https://doi.org/10.1103/PhysRevD.108.064002[Section II: null-tetrad curvature components and tetrad freedom]{ref}
Choosing directions adapted to a light ray, a horizon or an outgoing wave can make the relevant curvature components easier to identify. This is useful for radiation calculations and extracting <gravitational waves> from simulations. The components are scalars under coordinate changes but depend on the tetrad, so their signs, normalization and physical interpretation require a stated frame convention.
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