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

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.

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• Hyperbolic polytrope
• General Framework for the Spontaneous Scalarization of Regular Black Holes
• Traversable ghost wormholes
• Statistical complexity as a probe of mass and phase structure in compact objects