Dark-Sector Effects on the Phase Structure of Nonlinear Magnetic AdS Black Holes

Abstract

We investigate the effects of perfect fluid dark matter (PFDM) and a dark-energy field on the phase structure of a nonlinear magnetically charged Anti--de Sitter (NLMC--AdS) black hole. The full thermodynamic system is analyzed numerically, while exact critical points are obtained for the limiting cases. Small--large black hole (SBH/LBH) phase transitions emerge in both the limiting geometries and the full solution within the quintessence regime. Moreover, the critical ratio ${\rho }_c=P_c{v}_c/T_c$ differs from the standard Reissner--Nordström--AdS (RN--AdS)/van der Waals (vdW) value, ${\rho }_c=3/8$. Our results show that the dark-sector parameters significantly influence the strength and persistence of the first-order transition. In the quintessence regime, a stronger dark-energy contribution enhances the swallow-tail structure of the Gibbs free energy and increases the latent heat associated with SBH/LBH coexistence. In contrast, a larger magnitude of the PFDM parameter $|\lambda |$ progressively suppresses the swallow-tail structure and the corresponding first-order transition, eventually leading to a single-phase regime. In the phantom regime, the system instead exhibits spinodal behavior without phase coexistence. We also find that any nonzero $\lambda$ prevents the formation of a regular magnetic core. Finally, geometrothermodynamics (GTD) reproduces the phase structure through singularities of the thermodynamic curvature, while the associated critical scaling is consistent with results reported for black holes, cosmological horizons, and real fluids, pointing toward a broader universality of thermodynamic critical behavior.

Accepted for publication in Physics of the Dark Universe