Gravity of superheavy higher-dimensional global defects

Numerical solutions of Einstein's and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a (3 + 1)-dimensional core and a hedgehog scalar-field configuration in n = 3 extra dimensions. For sufficiently low symmetry-breaking scales eta, the solutions are characterized by a flat worldsheet geometry and a constant solid deficit angle in the extra dimensions, in agreement with previous work. For eta above the higher-dimensional Planck scale, we find that static-defect solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. We obtain an analytic solution for the metric of such inflating defects at large distances from the core. The three extra dimensions of the nonsingular solutions have a cigar geometry. Although our numerical solutions were obtained for defects of codimension n = 3, we argue that the conclusions are likely to apply to all it greater than or equal to 3.