Nonlinearly charged asymptotically massive Reissner-Nordstrom black holes in de Rham-Gabadadze-Tolley massive gravity theory

Two novel classes of nonlinearly charged black hole (BH) solutions are introduced in the context of massive gravity theory, which are coupled to the logarithmic and exponential theories of nonlinear electrodynamics. The solutions can produce one-horizon, two-horizon, extreme, and naked singularity BHs with the massive Reissner-Nordstrom BHs' asymptotic behavior. The BHs' conserved and thermodynamic quantities are calculated under the influence of both massive gravitons and nonlinear electrodynamics. Through a Smarr-type mass formula, it is shown that these quantities satisfy the standard form of the thermodynamical first law. Thermal stability of the massive BHs is investigated using the canonical ensemble and geometrical methods, separately. The first- and second-order phase transition points, and the size of those BHs which remain locally stable, are determined. Then, the results of these alternative approaches are compared. By calculating the Gibbs free energies, global stability or Hawking-Page phase transition of the BHs is studied. The points at which the phase transition takes place and the conditions under which the BHs are globally stable are characterized. The critical behavior of the BHs is studied in the extended phase space by considering the thermodynamic pressure proportional to the cosmological constant.