Extended phase space thermodynamics for dyonic black holes with a power Maxwell field

Abstract

In this paper, we investigate the thermodynamics of dyonic black holes with the presence of power Maxwell electromagnetic field in the extended phase space, which regards the cosmological constant $\mathrm{\ensuremath{\Lambda}}$ as a thermodynamic variable. For a generic power Maxwell black hole with the electric charge and magnetic charge, the equation of state is given as the function of rescaled temperature $\stackrel{\texttildelow{}}{T}$ in terms of other rescaled variables ${\stackrel{\texttildelow{}}{r}}_{+}$, $\stackrel{\texttildelow{}}{q}$, and $\stackrel{\texttildelow{}}{h}$, where ${r}_{+}$ is the horizon radius, $q$ is the electric charge, and $h$ is the magnetic parameter. For some values of $\stackrel{\texttildelow{}}{q}$ and $\stackrel{\texttildelow{}}{h}$, the phase structure of the black hole is uniquely determined. Moreover, the peculiarity of multiple temperature with some parameter configurations results in complex phase structures. Focusing on the power Maxwell Lagrangian with $\mathcal{L}(s)={s}^{2}$, we obtain the corresponding phase diagrams in the $\stackrel{\texttildelow{}}{h}\text{\ensuremath{-}}\stackrel{\texttildelow{}}{q}$ plane where the critical line extends to $\stackrel{\texttildelow{}}{h}=+\ensuremath{\infty}$. Then, we analyze the black holes' phase structure and critical behavior and display phase transition curves with different $\stackrel{\texttildelow{}}{h}$ in the $\stackrel{\texttildelow{}}{q}\text{\ensuremath{-}}\stackrel{\texttildelow{}}{T}$ plane. We also examine thermal stabilities of these black holes.