Einstein-AdS gravity coupled to modified arctan-electrodynamics, magnetic black hole thermodynamics and Joule-Thomson expansion

The metric and mass functions of Einstein-AdS gravity coupled to modified arctan-electrodynamics (proposed here) are obtained. We find corrections to the Reissner-Nordstrom solution. It is demonstrated that if the Schwarzschild mass is zero and as r -> 0 the asymptotic has the de Sitter core. Thermodynamics of magnetically charged black holes in Anti-de Sitter spacetime in an extended phase space, where the cosmological constant is treated as a pressure and the black hole mass is considered as the chemical enthalpy, is studied. It is shown that the black hole thermodynamics mimics the Van der Waals liquid-gas thermodynamics. The magnetic potential and vacuum polarization are calculated. We formulate the first law of black hole thermodynamics and proof that the generalized Smarr relation holds. The critical specific volume, temperature and pressure are evaluated and the critical behaviour of black holes is investigated. We calculate and study the Gibbs free energy and show that phase transitions take place. The local stability are studied by calculating the heat capacity. The black hole Joule-Thomson adiabatic expansion, cooling and heating phase transitions are investigated. We evaluate the Joule-Thomson coefficient and the inversion temperature.