On A 5-Dimensional Spinning Cosmic String

TL;DR

This paper numerically explores 5D spinning cosmic strings within the Einstein-Yang-Mills framework, analyzing their singularities, regular solutions with negative cosmological constant, and conditions for Gott space-time configurations.

Contribution

It provides the first numerical solutions of 5D spinning cosmic strings with a periodic extra dimension, examining their singularities, regularity conditions, and Gott space-time possibilities.

Findings

Singularities occur when the metric component approaches zero.

Negative cosmological constant yields regular solutions with acceptable angle deficit.

Opposite moving 5D strings can satisfy Gott conditions without helical time structures.

Abstract

We present a numerical solution of a stationary 5-dimensional spinning cosmic string in the Einstein-Yang-Mills (EYM) model, where the extra bulk coordinate $\psi$ is periodic. It turns out that when $g_{\psi\psi}$ approaches zero, i.e., a closed time-like curve (CTC) would appear, the solution becomes singular. When a negative cosmological constant is incorporated in the model, the solution becomes regular everywhere with angle deficit$<2\pi$. However, the cosmic string-like object has not all the desired asymptotic properties of the counterpart Abelian Nielsen-Olesen string. When we use a two point boundary value routine with the correct cosmic string features far from the core, then again a negative $\Lambda$ results in an acceptable string-like solution. We also investigated the possibility of a Gott space time structure of the static 5D cosmic string. The matching condition yields no obstruction for an effective angle deficit. Moreover, by considering the angular momentum in bulk space, no helical structure of time is necessary. Two opposite moving 5D strings could, in contrast with the 4D case, fulfil the Gott condition.