Extremal Einstein–Born–Infeld black holes in dilaton gravity

Abstract

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.