Gravitating global monopoles in extra dimensions and the brane world concept

TL;DR

This paper explores multidimensional global monopole configurations in brane world models, analyzing their structure, regularity, and ability to trap scalar matter, revealing new possibilities beyond traditional 5D models.

Contribution

It classifies all regular global monopole configurations in extra dimensions without specifying the potential shape, and demonstrates their capacity to trap scalar matter unlike RS2 models.

Findings

Monopoles can have infinite or finite radii depending on scalar field maximum.

Configurations can exhibit exponential or finite warp factor behavior.

Monopoles can trap scalar matter, unlike some existing models.

Abstract

Multidimensional configurations with Minkowski external space-time and a spherical global monopole in extra dimensions are discussed in the context of the brane world concept. The monopole is formed with a hedgehog-like set of scalar fields \phi^i with a symmetry-breaking potential V depending on the magnitude \phi^2 = \phi^i \phi^i. All possible kinds of globally regular configurations are singled out without specifying the shape of V(\phi). These variants are governed by the maximum value \phi_m of the scalar field, characterizing the energy scale of symmetry breaking. If \phi_m < \phi_cr (where \phi_cr is a critical value of \phi related to the multidimensional Planck scale), the monopole reaches infinite radii while in the ``strong field regime'', when \phi_m\geq \phi_cr, the monopole may end with a cylinder of finite radius or possess two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type 5D models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.