Horizonless Rotating Solutions in $(n+1)$-dimensional Einstein-Maxwell Gravity

TL;DR

This paper presents two classes of horizonless, asymptotically anti-de Sitter rotating solutions in higher-dimensional Einstein-Maxwell gravity, revealing their electromagnetic properties and calculating conserved quantities using the counterterm method.

Contribution

It introduces novel horizonless rotating solutions with magnetic fields in higher dimensions and analyzes their physical properties and conserved charges.

Findings

Solutions have no curvature singularities or horizons.

Net electric charge is proportional to rotation or boost parameters.

Counterterm method effectively removes divergences in conserved quantities.

Abstract

We introduce two classes of rotating solutions of Einstein-Maxwell gravity in $n+1$ dimensions which are asymptotically anti-de Sitter type. They have no curvature singularity and no horizons. The first class of solutions, which has a conic singularity yields a spacetime with a longitudinal magnetic field and $k$ rotation parameters. We show that when one or more of the rotation parameters are non zero, the spinning brane has a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a spacetime with an angular magnetic field and $% \kappa$ boost parameters. 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 brane. We also use the counterterm method inspired by AdS/CFT correspondence and calculate the conserved quantities of the solutions. We show that the logarithmic divergencies associated to the Weyl anomalies and matter field are zero, and the $r$ divergence of the action can be removed by the counterterm method.