Abstract
We study the thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying thermodynamical properties of these black holes. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on the thermodynamical structure of these black holes are investigated. Furthermore, some thermodynamical properties such as the volume expansion coefficient, speed of sound, and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.
Highlights
On the other hand, the coupling of the nonlinear sources and general relativity (GR) attracted much attention because of their specific properties
One of the special classes of the nonlinear electrodynamic sources is the power-law Maxwell invariant (PMI), of which the Lagrangian is an arbitrary power of the Maxwell Lagrangian [26,27,28,29,30]
In the case of PMI, it is evident that the signature of the temperature depends on the choices of the different parameters
Summary
The coupling of the nonlinear sources and GR attracted much attention because of their specific properties. One of the methods for obtaining van der Waals like critical points is through the use of the heat capacity with a relation between the cosmological constant and pressure [75]. This method has been employed in several papers and it was shown that its results are consistent with those obtained through regular methods. We want to study the thermal stability and phase transition in the context of the methods of GT and extended phase space for black holes in Einstein gravity with the PMI source in higher dimensions.
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