$$P$$ P – $$V$$ V criticality of topological black holes in Lovelock–Born–Infeld gravity

Abstract

To understand the effect of third order Lovelock gravity, P-V criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case β → ∞ is performed for the sevendimensional black holes. It is shown that, for the spherical topology, P-V criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of P-V criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss-Bonnet black holes. For k = 0, there would be no P-V criticality. Interesting findings occur in the case k = −1, in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the P-v diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of α, the entropy is always positive for any specific volume v. Since no P-V criticality exists for k = −1 in Einstein gravity and Gauss-Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss-Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and "swallow tail" behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research. a

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

“…Such a phenomenon (discussed further in the next section) has a dual interpretation for a boundary quantum field theory via the AdS/CFT correspondence and is related to a confinement/deconfinement phase transition in the dual quark gluon plasma [61]. For charged or rotating black holes one likewise observes a small/large black hole first order phase transition reminiscent of the liquid/gas transition of the van der Waals fluid [4,6,8,[15][16][17]21,22,27,28,33,39,[62][63][64][65][66][67][68][69][70][71].…”

Fractional-order phase transition of charged AdS black holes

“…In the extended phase space, one can construct a one-to-one correspondence between the thermodynamic quantities of AdS black hole and those of ordinary thermodynamic systems [21]. After that, many other AdS black holes and other interesting critical phenomena have been extensively explored [22][23][24][25][26][27][28][29][30][31][32].…”

Phase structure of the Born–Infeld–anti-de Sitter black holes probed by non-local observables

“…In [30], the Van der Waals-like phase transition was also observed in the Q − plane, where Q is electric charge and is the chemical potential. Treating the negative cosmological constant as the pressure P and its conjugate as the thermodynamical volume V , 1 the Van der Waals-like phase transition has also been observed in the P − V plane recently [31][32][33][34][35][36][37][38][39].…”