P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity

摘要

To understand the effect of third order Lovelock gravity, $P-V$ criticalityof topological AdS black holes in Lovelock-Born-Infeld gravity is investigated.The thermodynamics is further explored with some more extensions and detailsthan the former literature. A detailed analysis of the limit case$\beta\rightarrow\infty$ is performed for the seven-dimensional black holes. Itis shown that for the spherical topology, $P-V$ criticality exists for both theuncharged and charged cases. Our results demonstrate again that the charge isnot the indispensable condition of $P-V$ criticality. It may be attributed tothe effect of higher derivative terms of curvature because similar phenomenonwas 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 positivesolutions of critical points are found for both the uncharged and chargedcases. However, the $P-v$ diagram is quite strange. To check whether thesefindings are physical, we give the analysis on the non-negative definitenesscondition of entropy. It is shown that for any nontrivial value of $\alpha$,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, wecan relate our findings with the peculiar property of third order Lovelockgravity. The entropy in third order Lovelock gravity consists of extra termswhich is absent in the Gauss-Bonnet black holes, which makes the criticalpoints satisfy the constraint of non-negative definiteness condition ofentropy. We also check the Gibbs free energy graph and the "swallow tail"behavior can be observed. Moreover, the effect of nonlinear electrodynamics isalso included in our research.