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

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