Gravitating Global Monopoles in Extra Dimensions and the Brane World Concept

Multidimensional configurations with Minkowski external space-time and a spherically symmetric 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 φi with a symmetry-breaking potential V depending on the magnitude φ2 = φiφi . All possible kinds of globally regular configurations are singled out without specifying the shape of V (φ). These variants are governed by the maximum value φm of the scalar field, characterizing the energy scale of symmetry breaking. If φm < φcr (where φcr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii while in the “strong field regime”, when φm ≥ φcr , 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 five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.