The Newman--Penrose formalism resolves spacetime curvature into scalars by contracting the Weyl tensor with a complex null tetrad.
A complex null tetrad consists of two real null vectors and a complex-conjugate transverse pair, normalized so that the metric is reconstructed from their pairwise products.
For a null tetrad , one common curvature-sign convention defines . In an outgoing wave zone it encodes the two transverse gravitational wave polarizations as one complex scalar.
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The Newman–Penrose (NP) formalism is a mathematical framework used in the field of General Relativity and theoretical physics to study the properties of spacetime and gravitational fields. Developed by physicists Ezra Newman and Roger Penrose in the 1960s, this formalism is particularly useful for analyzing asymptotically flat spacetimes, such as those found in models of gravitational radiation and black hole physics.