Five dimensional Myers-Perry black holes with nonlinear electrodynamics

Employing higher order perturbation theory, we obtain five-dimensional rotating black holes in the Einstein gravity with nonlinear electrodynamics. We consider asymptotically flat charged rotating black hole solutions with two equal angular momenta and introduce the electric charge, q, as the perturbative parameter. We construct the extremal rapidly rotating black holes in the Einstein-nonlinear Maxwell theory in five dimensions, where we solve the equations of motion up to fourth order in q. We show that the perturbative parameters q and the nonlinearity parameter beta may modify the values of the physical quantities of the black holes. In particular, we find that beta may change the sign of the magnetic moment and the gyromagnetic ratio of the black hole spacetime when this parameter starts to depart strongly from the Maxwell limit. Finally, we obtain a generalized Smarr formula for the rotating black hole solutions.