Gravitational trapping potential with arbitrary extra dimensions

We extend a recently discovered, nonsingular 6-dimensional brane, solution to $D=4+n$ dimensions. As with the previous 6D solution the present solution provides a gravitational trapping mechanism for fields of spin 0, $\frac{1}{2}$, 1, and 2. There is an important distinction between two extra dimensions and $n$ extra dimensions that makes this more than a trivial extension. In contrast to gravity in $n>2$ dimensions, gravity in $n=2$ dimensions is conformally flat. The stress-energy tensor required by this solution has reasonable physically properties, and for $n=2$ and $n=3$ can be made to asymptotically go to zero as one moves away from the brane.