Magnetic Branes in $(n+1)$-dimensional Einstein-Maxwell-dilaton gravity

TL;DR

This paper constructs new higher-dimensional magnetic brane solutions in Einstein-Maxwell-dilaton gravity, analyzing their geometric properties, charges, and conserved quantities, revealing novel features of spinning and traveling magnetic sources.

Contribution

It introduces two classes of exact magnetic brane solutions with unique properties in Einstein-Maxwell-dilaton gravity, including non-asymptotic behavior and charge relations to rotation and velocity.

Findings

Solutions have no curvature singularities or horizons.

Spinning branes acquire electric charge proportional to rotation.

Traveling branes' charge relates to velocity of the branes.

Abstract

We construct two new classes of spacetimes generated by spinning and traveling magnetic sources in $(n+1)$-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. These solutions are neither asymptotically flat nor (A)dS. The first class of solutions which yields a $(n+1)$-dimensional spacetime with a longitudinal magnetic field and $k$ rotation parameters have no curvature singularity and no horizons, but have a conic geometry. We show that when one or more of the rotation parameters are nonzero, the spinning branes has a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a static spacetime with an angular magnetic field, and have no curvature singularity, no horizons, and no conical singularity. Although one may add linear momentum to the second class of solutions by a boost transformation, one does not obtain a new solution. We find that the net electric charge of these traveling branes with one or more nonzero boost parameters is proportional to the magnitude of the velocity of the branes. We also use the counterterm method and calculate the conserved quantities of the solutions.