Higher dimensional dilaton black holes in the presence of exponential nonlinear electrodynamics

Abstract

We examine the higher-dimensional action in which gravity is coupled to the exponential nonlinear electrodynamic field and a scalar dilaton field. We construct a new class of $n$-dimensional static and spherically symmetric black hole solutions of this theory in the presence of the dilaton potential with two Liouville-type terms. In the presence of two Liouville-type dilaton potentials, the asymptotic behavior of the obtained black holes is neither flat nor (A)dS. Due to the nonlinear nature of the electrodynamic field, the electric field has finite value near the origin where $r\ensuremath{\rightarrow}0$ and goes to zero as $r\ensuremath{\rightarrow}\ensuremath{\infty}$. Interestingly enough, we find that in the absence of the dilaton field, the electric field has a finite value at $r=0$, while as soon as the dilaton field is taken into account, the electric field diverges as $r\ensuremath{\rightarrow}0$. This implies that the presence of the dilaton field changes the behavior of the electric field near the origin. In the limiting case where the nonlinear parameter $\ensuremath{\beta}$ goes to infinity, our solutions reduce to dilaton black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. We compute the conserved and thermodynamic quantities of the solutions and show that these quantities satisfy the first law of black hole thermodynamics on the horizon.