Thermodynamic Phase Structure and Shadow Analysis of 4D AdS Skyrmion Black Holes

This study systematically analyzes the Einstein-Skyrme black hole, also called skyrmion black hole, solution in four-dimensional AdS spacetime, focusing on its geometric, thermodynamic, and optical properties. The black hole solution is characterized by the mass parameter, cosmological constant, and skyrmion parameters (K and λ), which significantly influence its horizon structure. Increasing these parameters reduces the event horizon radius and, in certain cases, prevents horizon formation. The thermodynamic properties examined include mass, temperature, entropy, specific heat, and Gibbs free energy. The black hole mass exhibits non-monotonic behavior, and the Hawking temperature follows a characteristic rise and fall influenced by skyrmion parameters. Stability analysis reveals second-order phase transitions, with smaller black holes generally more stable. The Gibbs free energy remains positive, indicating global thermodynamic instability. We extend the analysis to the thermodynamic phase space of the black hole that exhibits Van der Waals-like phase transitions, with critical points consistent with the Van der Waals equation. Optical properties and shadow thermodynamics are also explored, showing that skyrmion parameters significantly alter photon trajectories for small black holes, and the shadow thermal profile is consistent with the temperature and shadow radius. These findings provide deeper insights into the interplay between skyrmions and black hole physics in AdS spacetime.