Extremal Myers-Perry black holes coupled to Born-Infeld electrodynamics in odd dimensions

Employing higher order perturbation theory, we find a new class of perturbative extremal rotating black hole solutions with Born-Infeld electric charge in odd D-dimensional spacetime. The seed solution is an odd dimensional extremal Myers-Perry black hole with equal angular momenta to which a perturbative nonlinear electric Born-Infeld field charge q is added maintaining the extremality condition. The perturbations are performed up to third order. We also study some physical properties of these black holes. In particular, it is shown that the values of the gyromagnetic ratio of the black holes are modified by the perturbative parameter q and the Born-Infeld parameter {\beta}.