Merger of Widom lines when Gauss–Bonnet coupling exits the triple-point regime

Determine whether, in six-dimensional charged Gauss–Bonnet anti–de Sitter black holes, varying the Gauss–Bonnet coupling α outside the parameter range that supports a triple point causes the two Widom lines in the supercritical regime (defined via the Lee–Yang analytic continuation of Gibbs free energy singularities) to merge into a single Widom line, and comprehensively map the evolution of the supercritical structure across the α parameter space to characterize this transition.

Background

The paper applies Lee–Yang theory to charged Gauss–Bonnet AdS black holes to paper supercritical behavior. In five dimensions, which features a single critical point, the supercritical region is divided by one Widom line into small-black-hole-like and large-black-hole-like sectors. In six dimensions, for α values that admit a triple point, the authors find two distinct Widom lines partitioning the supercritical region into three sectors corresponding to small, intermediate, and large black hole phases.

To assess the generality of this two–Widom–line structure, the authors propose a conjecture about how the supercritical phase boundaries evolve as α is varied. Specifically, they suggest that when α lies outside the parameter regime supporting a triple point, the system should revert to a single critical point and the two Widom lines should merge into one, reproducing a VdW-like supercritical structure. They emphasize that a comprehensive scan of the α parameter space to map this structural evolution remains to be carried out.