Magnetic Strings in Einstein-Born-Infeld-Dilaton Gravity

TL;DR

This paper introduces a new class of spinning magnetic string solutions in Einstein-dilaton gravity with Liouville potential, featuring unique properties like no singularities or horizons, and explores their conserved quantities and generalizations to higher dimensions.

Contribution

It presents novel spinning magnetic string solutions with nonlinear electromagnetic fields in Einstein-dilaton gravity, including their conserved quantities and higher-dimensional extensions.

Findings

Solutions have no curvature singularity or horizon.

Spinning solutions acquire electric charge proportional to rotation.

Conserved quantities are calculated using the counterterm method.

Abstract

A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. These solutions have no curvature singularity and no horizon, 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. Although the asymptotic behavior of these solutions are neither flat nor (A)dS, we calculate the conserved quantities of these solutions by using the counterterm method. We also generalize these four-dimensional solutions to the case of $(n+1)$-dimensional rotating solutions with $k\leq[n/2]$ rotation parameters, and calculate the conserved quantities and electric charge of them.