Magnetic dilaton rotating strings in the presence of logarithmic nonlinear electrodynamics

Abstract

We consider the Einstein-dilaton gravity in the presence of logarithmic nonlinear electrodynamics, and find a new class of four-dimensional spinning magnetic dilaton string solutions which produces a longitudinal nonlinear electromagnetic field. We find that these solutions have no curvature singularity and no horizon, but have a conic geometry. The net electric charge of the spinning string is proportional to the rotating parameter and the electric field only exists when the rotation parameter does not vanish. We investigate the effects of the nonlinearity as well as the dilaton field on the physical properties of the spacetime. Because of the presence of the dilaton field, the asymptotic behavior of the solutions are neither flat nor (anti)-de Sitter. We find the deficit angle of the spacetime and investigate the effects of dilaton and nonlinear electrodynamics on the value of the deficit angle. We use the counterterm method to calculate the conserved quantities of the solutions. Furthermore, we extend our study to the higher dimensions and obtain the $$(n+1)$$ -dimensional magnetic rotating dilaton strings with $$k\le [n/2]$$ rotation parameters and calculate electric charge and conserved quantities of the solutions.