Rotating black holes in general relativity coupled to nonlinear electrodynamics

Highlights: • We report an exact spherically symmetric magnetically charged black hole solution to general relativity (GR) coupled to nonlinear electrodynamics (NED). • Further, we generalize its rotating spacetime using the revised Newman–Janis algorithm, and calculate the thermodynamic quantities, such as, the mass, Hawking temperature, entropy, heat capacity and free energy. • In the canonical ensemble, smaller magnetically charged rotating black holes ($r_{+}<r_c$) are thermodynamically preferred than the large black holes. • The Hawking–Page-type phase transition is not conceivable because the free energy is positive for all the parameter space. • Interestingly, the radiating counterpart renders a generalization of Carmeli's spacetime as well as Vaidya's spacetime in the appropriate limits. We find an exact spherically symmetric magnetically charged black hole solution to general relativity (GR) coupled to nonlinear electrodynamics (NED) with an appropriate Lagrangian density. In turn, starting with this spherical black hole as a seed metric, we construct a rotating spacetime, a modification of Kerr black hole, using the revised Newman–Janis algorithm that depends on mass, spin, and a NED parameter $g$. We find an exact expression for thermodynamic quantities of the black holes like the mass, Hawking temperature, entropy, heat capacity, and free energy expressed in terms of horizon radius, and they show significant deviations from the Kerr case owing to NED. We also calculate analytical expressions for effective Komar mass and angular momentum for the rotating black hole and demonstrate that the Komar conserved quantity corresponding to the null Killing vector at horizon obeys $K_{\chi }=2S_{+}{T}_{+}.$ The radiating counterpart renders a generalization of Carmeli's spacetime as well as Vaidya's spacetime in the appropriate limits.