Thermodynamics and phase transitions of nonlinearly scalarized black holes in Einstein-scalar-Gauss-Bonnet theory

We investigate the thermodynamic properties of static nonlinearly scalarized black holes in Einstein-scalar-Gauss-Bonnet theory with polynomial coupling functions. Based on the scalarized solutions constructed previously, we compute thermodynamical quantities of these scalarized black holes. Moreover, we examine the first law of black hole thermodynamics and consider the phase transitions between Schwarzschild and scalarized black holes. It shows that a phase transition from Schwarzschild black hole to scalarized black hole is a first-order with non-zero latent heat.