Abstract
In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We also show how considering cosmological constant, nonlinearity and Lovelock parameters as thermodynamical variables will modify Smarr formula and first law of thermodynamics. In addition, we study the behavior of universal ratio of $\frac{P_{c}v_{c}}{T_{c}}$ for different values of nonlinearity power of electrodynamics as well as the Lovelock coefficients.
Highlights
In context of AdS/CFT correspondence, it was proposed that variation of cosmological constant corresponds to varying the number of colors in the boundary field theory of Yang-Mills with chemical potential interpretation [1,2,3,4]
One may consider the cosmological constant as a thermodynamical pressure to extend the phase space and modify the first law of black holes thermodynamics [12, 13]
We investigate the effects of both nonlinearity of the electrodynamic models and Lovelock parameters on the phase diagrams and the critical values
Summary
In context of AdS/CFT correspondence, it was proposed that variation of cosmological constant corresponds to varying the number of colors in the boundary field theory of Yang-Mills with chemical potential interpretation [1,2,3,4]. One is motivated to study these theories (which in this paper we have considered logarithmic [19] and exponential forms [20]) and the nonlinearity effects of electromagnetic field on critical values representing phase transition of black holes. The Lagrangian of Lovelock gravity is obtainable through the use of the low energy effective action of string theory [18] One can take this fact into account that modification of Einstein gravity may change the conserved quantities of black holes and it is inevitable to see that critical values and phase transition may depend on the choice of gravity model.
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