Construction of a complex null tetrad

In the context of general relativity and the study of spacetime, a null tetrad is a mathematical construct used to facilitate the analysis of light rays and the behavior of null (light-like) geodesics. A null tetrad consists of four vectors, typically denoted as \( l^\mu, n^\mu, m^\mu, \) and \( \bar{m}^\mu \), which satisfy certain orthogonality and normalization conditions.