Thermodynamics of novel black holes in massive gravity coupled to nonlinear electrodynamics

By introducing a static and spherically symmetric geometry, we have solved the coupled electromagnetic and gravitational field equations in the presence of both, massive gravitons and nonlinear electrodynamics. The exact solutions show that massive gravity theory admits two novel classes of nonlinearly charged asymptotically AdS black holes. The black holes' electric charge, mass, and other thermodynamic quantities have been calculated. Then, by use of a Smarr-type mass formula, it has been proved that the thermodynamical first law is valid for both the new massive black hole solutions. The black hole local stability has been investigated by use of the canonical ensemble and geometrical methods, separately. Through comparison of the results, we found that they are compatible provided that the HEPM or QII thermodynamic metrics are used. Global stability and Hawking-Page phase transition points have been studied by use of the grand canonical ensemble method and regarding the Gibbs free energy of the black holes.