Ehrenfest Scheme of Higher Dimensional Topological AdS Black Holes in The Third Order Lovelock-Born-Infeld Gravity

Abstract

Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in Lovelock-Born-Infeld gravity. In particular, we give an explicit expression of the universal number χ=\frac{P_c v_c}{T_c} in terms of the space dimension $n$. Then, we examine the phase transitions at the critical points of such topological black holes for 6 \leq n \leq 11 as required by the physical condition of the thermodynamical quantities. More precisely, the Ehrenfest equations have been checked revealing that the black hole system undergoes a second phase transition at the critical points.

18 pages, latex with 10 figures, titled modified, section added, typos corrected, accepted for publication in International Journal of Geometric Methods in Modern Physics (2015)