Microstructure of charged AdS black hole via $P-V$ criticality

Understand

We suggest a new thermodynamic curvature, constructed via adiabatic compressibility, for examining the internal microstructure of charged black holes in an anti-de Sitter (AdS) background.

• We analyze the microscopic properties of small-large phase transition of black holes with pressure and volume as the fluctuation variables.
• We observe that strong repulsive interactions dominate among the micro-structures of near extremal small black holes, and the thermodynamic curvature diverges to positive infinity for the extremal black holes.
• At the critical point, however, thermodynamic curvature diverges to negative infinity.