Configurational entropy of anti-de Sitter black holes

TL;DR

This paper introduces a method to compute the configurational entropy of AdS-Schwarzschild black holes, linking it to phase transitions and stability, and verifies its consistency with known behaviors in flat space black holes.

Contribution

A new technique for defining and calculating the configurational entropy of AdS black holes, connecting it to thermodynamic stability and phase transitions.

Findings

Configurational entropy increases with temperature, indicating black hole dominance.

The method aligns with the Hawking-Page phase transition.

Smaller flat space black holes are more unstable, consistent with physical expectations.

Abstract

Recent studies indicate that the configurational entropy is an useful tool to investigate the stability and (or) the relative dominance of states for diverse physical systems. Recent examples comprise the connection between the variation of this quantity and the relative fraction of light mesons and glueballs observed in hadronic processes. Here we develop a technique for defining a configurational entropy for an AdS-Schwarzschild black hole. The achieved result corroborates consistency with the Hawking-Page phase transition. Namely, the dominance of the black hole configurational entropy will be shown to increase with the temperature. In order to verify the consistency of the new procedure developed here, we also consider the case of black holes in flat space-time. For such a black hole, it is known that evaporation leads to instability. The configurational entropy obtained for the flat space case is thoroughly consistent with the physical expectation. In fact, we show that the smaller the black holes, the more unstable they are. So, the configurational entropy furnishes a reliable measure for stability of black holes.