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 Λ. The defect has a (p-1)-dimensional core (brane) and a ``hedgehog'' scalar field configuration in the n extra dimensions. For Λ=0 and $n>2,$ the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Λ>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 Λ<0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for $n=1$ and by Gregory for $n=2.$