Magnetic black holes within Einstein-AdS gravity coupled to nonlinear electrodynamics, extended phase space thermodynamics and Joule--Thomson expansion

Einstein's gravity in AdS space coupled to nonlinear electrodynamics is studied. We analyse the metric, mass functions and corrections to the Reissner--Nordström solution. Magnetic black holes thermodynamics in extended phase space is investigated. We formulate the first law of black hole thermodynamics showing that the generalized Smarr relation holds. The black hole stability is studied by evaluating the Gibbs free energy and heat capacity. To study the cooling and heating phase transitions of black holes we consider the Joule--Thomson isenthalpic expansion. The Joule--Thomson coefficient and the inversion temperature are calculated.