Abstract
Considering the unexpected similarity between the thermodynamic features of charged AdS black holes and that of the van der Waals fluid system, we calculate the number densities of black hole micromolecules and derive the thermodynamic scalar curvature for the small and large black holes on the co-existence curve based on the so-called Ruppeiner thermodynamic geometry. We reveal that the microscopic feature of the small black hole perfectly matches that of the ideal anyon gas, and that the microscopic feature of the large black hole matches that of the ideal Bose gas. More importantly, we investigate the issue of molecular potential among micromolecules of charged AdS black holes, and point out explicitly that the well-known experiential Lennard-Jones potential is a feasible candidate to describe interactions among black hole micromolecules completely from a thermodynamic point of view. The behavior of the interaction force induced by the Lennard-Jones potential coincides with that of the thermodynamic scalar curvature. Both the Lennard-Jones potential and the thermodynamic scalar curvature offer a clear and reliable picture of microscopic structures for the small and large black holes on the co-existence curve for charged AdS black holes.
Highlights
It is widely accepted that black holes are the most probable candidate to provide a bridge between a possible quantum theory of gravity and the classical general relativity, and that they likely represent one of the most intriguing macroscopic objects
Based on the Ruppeiner thermodynamic geometry, we give the exact expressions of the number density and the thermodynamic scalar curvature for the small and large black holes on the coexistence curve
The behavior of the interaction force induced by the molecular potential coincides with that of the thermodynamic scalar curvature
Summary
It is widely accepted that black holes are the most probable candidate to provide a bridge between a possible quantum theory of gravity and the classical general relativity, and that they likely represent one of the most intriguing macroscopic objects. The most important discovery in this active field is [6] the phase transition of black holes in the anti–de Sitter (AdS) spacetime This result has been extended to a variety of more complicated cases, especially to the case of charged AdS black holes in which an analytical analogy with the van der Waals fluid system can be made [7,8,9,10,11]. The so-called Ruppeiner thermodynamic geometry provides [14,15,16] phenomenologically a potential description about the types of interaction among micromolecules both in an ordinary thermodynamic system and in a black hole system.
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