Thermodynamics and Phase Transitions of Nonlinear Electrodynamics Black Holes in an Extended Phase Space (1808.04506v2)

Abstract: We investigate the thermodynamic behavior of nonlinear electrodynamics (NLED) black holes in an extended phase space, which includes the cosmological constant $\Lambda=-3/l^{2}$ and dimensionful couplings $a$ in NLED as thermodynamic variables. For a generic NLED black hole with the charge $Q$, we find that the Smarr relation is satisfied in the extended phase space, and the state of equation can be written as $Tl=\tilde{T}\left( r_{+}/l,Q/l,al^{-c} \right) $, where $\left[ a\right] =L^{c}$, and $T$ and $r_{+}$ are the temperature and horizon radius of the black hole, respectively. For some values of $Q/l$ and $al^{-c}$, the phase structure of the black hole is uniquely determined. Focusing on Born-Infeld and iBorn-Infeld AdS black holes, we obtain the corresponding phase diagrams in the $a/l^{2}$-$Q/l$ plane, which provides a new viewpoint towards the black holes' phase structure and critical behavior. For Born-Infeld black holes, the critical line and the region, where a reentrant phase transition occurs, in the $a/l^{2}$-$Q/l$ plane are both finite and terminate at $\left{ \tilde{a}{c}\text{, }\tilde{Q}{c}\right} \simeq\left{ 0.069\text{, }0.37\right} $. However for iBorn-Infeld black holes, the critical line and the reentrant phase transition region in the $a/l^{2}$-$Q/l$ plane are semi-infinite and extend to $Q/l=\infty$. We also examine thermal and electrical stabilities of Born-Infeld and iBorn-Infeld AdS black holes.