Gravitational localization of all local fields on the brane

We present a new (p−1)-brane solution to Einstein's equations in a general spacetime dimension. This solution is a natural generalization of the stringlike defect solution with codimension 2 in 6 spacetime dimensions, which has been recently discovered by Gogberashvili and Singleton, to a general (p−1)-brane solution with codimension n in general D=p+n spacetime dimensions. It is shown that all the local fields are localized on the brane only through the gravitational interaction although this solution does not have a warp factor and takes a finite value in the radial infinity. Thus, this solution is a solution in an arbitrary spacetime dimension realizing the idea of “gravitational trapping” of the whole bulk fields on the brane within the framework of a local field theory. Some problems associated with this solution and localization are pointed out.