Weyl scalars

In the Newman–Penrose (NP) formalism of general relativity, Weyl scalars refer to a set of five complex scalars ${\displaystyle \{\Psi _{0},\Psi _{1},\Psi _{2},\Psi _{3},\Psi _{4}\}}$ which encode the ten independent components of the Weyl tensors of a four-dimensional spacetime.

Given a complex null tetrad ${\displaystyle \{l^{a},n^{a},m^{a},{\bar {m}}^{a}\}}$ and with the convention ${\displaystyle \{(-,+,+,+);l^{a}n_{a}=-1\,,m^{a}{\bar {m}}_{a}=1\}}$, the Weyl-NP scalars are defined by

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