Rational nonlinear electrodynamics of AdS black holes and extended phase space thermodynamics

Abstract: The critical behavior of magnetically charged by rational nonlinear electrodynamics (RNED) AdS black holes in an extended phase space is investigated. The cosmological constant is considered as a thermodynamic pressure and the black hole mass is identified with the chemical enthalpy. The analogy with the Van der Waals liquid-gas system is found and the critical exponents coincide with those of the Van der Waals system. The thermodynamics of RNED-AdS black holes and phase transitions are studied. A new thermodynamic quantities conjugated to the nonlinear parameter of RNED and a magnetic charge are defined. It is demonstrated the consistency of the first law of black hole thermodynamics and the Smarr formula.