Universal Supercritical Behavior in Global Monopole-Charged AdS Black Holes

TL;DR

This paper analytically studies the universal supercritical behavior and Widom line in charged AdS black holes with a global monopole, demonstrating universal scaling laws unaffected by monopole parameters.

Contribution

It derives closed-form expressions for Widom and crossover lines and confirms universal supercritical scaling in both ensembles.

Findings

Monopole parameter shifts critical points but preserves universal scaling.

Closed-form expressions for Widom and crossover lines are obtained.

Universal supercritical phase diagrams are numerically verified.

Abstract

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 $\Omega$ 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 numerically verify this using the supercritical crossover lines $L^\pm$ and show the universal scaling laws and the complete supercritical phase diagrams.