Multidimensional Global Monopole and Nonsingular Cosmology

TL;DR

This paper investigates higher-dimensional global monopoles in general relativity, revealing their asymptotic flatness, horizon structures, and potential cosmological applications, including nonsingular models and generalizations of known 4D solutions.

Contribution

It extends the analysis of global monopoles to higher dimensions, exploring their spacetime structures, horizons, and cosmological implications, including analytical descriptions and numerical estimations.

Findings

Monopoles are asymptotically flat with a solid angle defect for certain parameters.

Existence of cosmological horizons in specific parameter ranges.

Nonsingular cosmological models with potential viability in 3D cases.

Abstract

We consider a spherically symmetric global monopole in general relativity in $(D=d+2)$-dimensional spacetime. The monopole is shown to be asymptotically flat up to a solid angle defect in case $\gamma < d-1$, where $\gamma$ is a parameter characterizing the gravitational field strength. In the range $d-1< \gamma < 2d(d+1)/(d+2)$ the monopole space-time contains a cosmological horizon. Outside the horizon the metric corresponds to a cosmological model of Kantowski-Sachs type, where spatial sections have the topology ${\R\times \S}^d$. In the important case when the horizon is far from the monopole core, the temporal evolution of the Kantowski-Sachs metric is described analytically. The Kantowski-Sachs space-time contains a subspace with a $(d+1)$-dimensional Friedmann-Robertson-Walker metric, and its possible cosmological application is discussed. Some numerical estimations in case $d=3$ are made showing that this class of nonsingular cosmologies can be viable. Other results, generalizing those known in the 4-dimensional space-time, are derived, in particular, the existence of a large class of singular solutions with multiple zeros of the Higgs field magnitude.