Gravity of higher-dimensional global defects

Solutions of Einstein’s equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant $\Lambda .$ The defect has a $\left(p-1\right)$-dimensional core (brane) and a “hedgehog” scalar field configuration in the n extra dimensions. For $\Lambda =0\mathrm{}$ and $n>\mathrm{}2,$ the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For $\Lambda >0,$ one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For $\Lambda <0,$ one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for $n=1\mathrm{}$ and by Gregory for $n=2.\mathrm{}$