The effects of nonlinear Maxwell source on the magnetic solutions in Einstein-Gauss-Bonnet gravity

Abstract

Considering both the power Maxwell invariant source and the Einstein--Gauss--Bonnet gravity, we present a new class of static solutions yields a spacetime with a longitudinal nonlinear magnetic field. These horizonless solutions have no curvature singularity, but have a conic geometry with a deficit angle $δϕ$. In order to have vanishing electromagnetic field at spatial infinity, we restrict the nonlinearity parameter to $s>1/2$. Investigation of the energy conditions show that these solutions satisfy the null, weak and strong energy conditions simultaneously, for $s>1/2$, and the dominant energy condition is satisfied when $s \in ({1/2,1}]$. In addition, we look for about the effect of nonlinearity parameter on the energy density and also deficit angle, and find that these quantities are sensitive with respect to variation of nonlinearity parameter. We find that for special values of nonlinearity parameter, two important subclass of solutions, so-called conformally invariant Maxwell and BTZ-like solutions, with interesting properties, emerge. Then, we generalize the static solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. We also use the counterterm method to compute the conserved quantities of these spacetimes such as mass, angular momentum, and find that these conserved quantities do not depend on the nonlinearity parameter.