Hyper-Charged Vortices and Strings with Signature Change Horizon

TL;DR

This paper explores exact solutions in Einstein-Maxwell-Dilaton gravity coupled with vortices, revealing horizons at exponentially large scales and unique metric behaviors, with implications for higher-dimensional string solutions.

Contribution

It introduces a class of exact solutions involving self-dual vortices coupled to gravity, showing how horizons form at large scales and analyzing their properties in various dimensions.

Findings

Horizon scale exponentially depends on vortex core size and Planck length.

Metric deviates logarithmically from flat space in the intermediate region.

Divergence of energy and charge integrals at the signature change horizon.

Abstract

We show that self-dual Nielsen Olesen (NO) vortices in $3$ dimensions give rise to a class of exact solutions when coupled to Einstein Maxwell Dilaton gravity obeying the Majumdar-Papapetrou(MP) relation between gravitational and Maxwell couplings , provided certain Chern-Simons type interactions are present. The metric may be solved for explicitly in terms of the NO vortex function and becomes degenerate at scales $r_H \sim l_S exp(\frac{l_S}{l_P})$ where $l_S$ is the vortex core size and $l_P$ the Planck length. For typical $l_S\geq 10^4 l_P$ the horizon is thus pushed out to exponentially large scales. In the intermediate asymptotic region (IAR) $l_S<<r<<r_H$ there is a logarithmic deviation of the metric from the flat metric and of the electric field from that of a point charge (which makes it decrease {\it{slower}} than $r^{-1}$ :hence the prefix hyper). In the IAR the ADM energy and charge integrals increase logarithmically with the distance from the core region and finally diverge at the signature change horizon. String solutions in $4+p$ dimensions are obtained by replacing the Maxwell fiel0d by an antisymmetric tensor field (of rank $2+p$) and have essentially similar properties with $r_H \sim l_S exp((\frac{l_S}{l_P})^{2+p})$ and with the antisymmetric charge playing the role of the topological electric charge .