Universal Supercritical Behavior in Global Monopole-Charged AdS Black Holes

We analytically investigate the Widom line and universal supercritical crossover for charged AdS black holes threaded by a global monopole. We compute thermodynamic variables in both the extended and canonical ensembles. We derive the scaled variance $Ω$ using the Gibbs free energy and locate the Widom line as the extrema of this. Using mean-field expansion of the equation of state near criticality, we obtain closed-form expressions for the Widom line and the two branching crossover lines $L^\pm$. We show that the monopole parameter shifts the critical parameters but does not change the mean-field universal scaling: the leading linear term and the nonanalytic correction remain universal in both ensembles. We also verify this with numerical computation and show the Widom line and the two branching crossover lines $L^\pm$.

💡 Research Summary

The paper investigates the supercritical behavior of charged anti‑de Sitter (AdS) black holes that carry a global monopole, focusing on the emergence of a Widom line and the associated bifurcating crossover branches (denoted L⁺ and L⁻). The authors work in both the extended phase‑space ensemble, where the cosmological constant is promoted to a thermodynamic pressure, and the canonical ensemble, where the pressure (or equivalently the AdS radius) is held fixed and the electric charge is allowed to fluctuate.

First, the authors review the charged AdS black‑hole solution with a global monopole. The monopole introduces a solid‑angle deficit parameter ζ (with ζ² = 8πζ₀²) that rescales the angular part of the metric by a factor (1‑ζ²). After a convenient rescaling of the time coordinate, radial coordinate, mass and charge, the metric takes the simple form
ds² = –f(r)dt² + dr²/f(r) + r²(1‑ζ²)dΩ²,
with f(r)=1‑2M/(1‑ζ²)r + Q²/(1‑ζ²)²r² + r²/L². This factor directly modifies all thermodynamic quantities.

In the extended ensemble the pressure is P = 3/(8πL²). The temperature, entropy, thermodynamic volume and electric potential become
T = (1/(4πr₊))