Equilibrium Gibbs Bifurcations of Bardeen-AdS Black Holes at Fixed Pressure

Abstract: In the direct horizon convention, the fixed-pressure Gibbs curve of the four-dimensional Bardeen-AdS black hole passes through an intermediate sequence between the Reissner-Nordstrom-AdS swallow-tail class and the single-branch regime as the regularization scale is increased. The on-shell curve is classified by its turning points and self-intersections, followed by local heat-capacity filtering and construction of the lower Gibbs envelope over stable branches. The deformation is resolved into three boundaries: g_*(P), where the RN-AdS-like topology is lost; g_c(P), where the c-shaped sector begins; and g_s(P), where the positive-temperature multibranch structure terminates. A reduced-variable analysis shows that these boundaries are controlled by the dimensionless combination 8 pi P g^2, accounting for their inverse-square-root pressure dependence and giving an analytic value for the final single-branch boundary. The equilibrium construction further shows that stable small/large coexistence can survive the first topology change, whereas the representative c-shaped regime has no stable crossing. Within the direct convention, these results define a Gibbs bifurcation structure for Bardeen-AdS thermodynamics.