Slowly rotating dilatonic black holes with exponential form of nonlinear electrodynamics

Abstract

The generalization of the four-dimensional Kerr–Newman black holes to include the nonlinear electrodynamics has been one of the famous problems in black hole physics. In this paper, we address the effects of the small rotation parameter on the exact black hole solutions of Einstein-dilaton gravity coupled to the exponential nonlinear electrodynamics. We find a new stationary black hole solutions of this theory, in the limit of small angular momentum, and in the presence of Liouville-type potential for the dilaton field and an arbitrary value of the dilaton coupling constant. We compute the angular momentum and the gyromagnetic ratio of these rotating dilaton black holes. Interestingly enough, we find that the nonlinearity of the electrodynamics do not affect the angular momentum and the gyromagnetic ratio of the spacetime, while in contrast, the dilaton field can modify the angular momentum as well as the gyromagnetic ratio of the rotating black holes. We find the gyromagnetic ratio as \(g=6/(3-\alpha ^2)\), where \(\alpha \) is the coupling constant of the dilaton and the electrodynamic fields. For \(\alpha =0\), we arrive at \(g=2\), which is the gyromagnetic ratio of the Kerr–Newman black holes in four dimensions.