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

TL;DR

This paper introduces a complexity factor for black holes within the Newman-Penrose formalism, providing a thermodynamic interpretation related to pressure and Van der Waals-like behavior at the event horizon.

Contribution

It defines and analyzes a new complexity factor for black holes using Newman-Penrose formalism, linking it to thermodynamics and black hole equations of state.

Findings

Complexity factor interpreted at the event horizon.

Thermodynamic interpretation involving pressure.

Relation to Van der Waals-like equation of state.

Abstract

In this work, we introduce the {\it 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.