Complexity factor for black holes in the framework of the Newman–Penrose formalism

In this work, we introduce the {\it complexity factor} in context of self--gravitating fluid distributions for case black holes by employing Newman-Penrose formalism. particular, working with spherically symmetric and static AdS holes, show that factor can be interpreted a natural way at event horizon. Specifically, thermodynamic interpretation aforementioned terms pressure partially supporting Van der Waals-like equation state is given.