Magnetic Strings in Dilaton Gravity

TL;DR

This paper introduces new magnetic rotating solutions in Einstein-Maxwell-dilaton gravity with Liouville potential, revealing horizonless, conic geometries with electric fields linked to rotation and velocity, and extends to higher dimensions.

Contribution

It presents novel classes of magnetic rotating solutions in four and higher dimensions within Einstein-dilaton gravity with Liouville potential, including their properties and conserved quantities.

Findings

Solutions have no curvature singularity or horizons.

Spinning strings acquire electric charge proportional to rotation.

Higher-dimensional solutions can be horizonless with conic singularities.

Abstract

First, I present two new classes of magnetic rotating solutions in four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. The first class of solutions yields a 4-dimensional spacetime with a longitudinal magnetic field generated by a static or spinning magnetic string. I find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. The net electric charge of the strings in these spacetimes is proportional to their velocities. Second, I obtain the ($n+1$)-dimensional rotating solutions in Einstein-dilaton gravity with Liouville-type potential. I argue that these solutions can present horizonless spacetimes with conic singularity, if one chooses the parameters of the solutions suitable. I also use the counterterm method and compute the conserved quantities of these spacetimes.