Extremal Einstein-Born-Infeld black holes in dilaton gravity

Motivated by considerable interests of Myers-Perry black holes, we employ the perturbative method to obtain a family of extremal charged rotating black hole solutions in odd dimensional Einstein-Born-Infeld-dilaton gravity. We start with an extremal Myers-Perry black hole with equal angular momenta, and then by adding the dilaton field and the nonlinear Born-Infeld electrodynamics, we find an extremal nonlinearly charged rotating black holes. The perturbative parameter is assumed to be the electric charge q and the perturbations are performed up to the third order. We then study the physical properties of these Born-Infeld-dilaton black holes. In particular, we show that the perturbative parameter, q, the dilaton coupling constant, α, and the Born-Infeld parameter, β, modify the Smarr formula and the values of the gyromagnetic ratio of the extremal charged rotating black holes.