Thermodynamics of Ayón-Beato–García–AdS black holes in 4D Einstein–Gauss–Bonnet gravity

• Published in: European physical journal plus 2022-02, Vol.137 (2), p.278, Article 278
• Main Authors: Belhaj, A., Sekhmani, Y.
• Format: Article
• Language: English
• Subjects: Applied and Technical Physics; Atomic; Black holes; Complex Systems; Condensed Matter Physics; Curvature; Gibbs free energy; Gravitational waves; Gravity; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Phase transitions; Physical properties; Physics; Physics and Astronomy; Regular Article; Spacetime; Specific heat; Theoretical; Theory of relativity; Transition points
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-022-02495-z

Within a family of Ayón-Beato–García black holes in four-dimensional Einstein–Gauss–Bonnet (EGB) gravity in Anti-de Sitter space-time geometries, we study various thermodynamical aspects by computing the relevant quantities which include the mass, the Hawking temperature, the entropy, the heat capacity, and the Gibbs free energy. We find that the heat capacity is discontinuous at critical values of the radial coordinate, with sign changes that hint at transitions between small and large black holes near such critical values. After providing evidence that such solutions exhibit a P – v criticality, we analyze the Gibbs free energy and show that it shares similarities with the Van der Waals phase transitions. In order to confirm the second-order nature of the phase transition points, we study the thermodynamical curvature of the Ruppeiner metric, finding that the singular points of such a curvature coincide with the ones at which the heat capacity diverges.