Stability and phase transition of black holes in Einstein-Maxwell-dilaton gravity

In this research, we study black hole stability and phase transition in Einstein-Maxwell-dilaton (EMD) gravity. A dilaton field is non-minimally related to the Maxwell field in the EMD gravity and is an intriguing alternative for General Relativity. By using the thermodynamic laws of the black holes, temperature, entropy, heat capacity, pressure, critical points and Gibbs free energy of charged static dilaton black holes in EMD gravity were all thoroughly explored and effects of dilaton constant on these quantities are studied and the results are compared with Schwarzschild, Reissner-Nordström, and Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black holes. In other cases, the system has stable and unstable areas. Since the heat capacity is discontinuous, the system experiences a phase transition, and Van der Waals-like phase transitions occur between the small and large black holes. It has been observed that the heat capacity for the GMGHS and Schwarzschild black holes is always negative, making these systems unstable.