Exact gravitational field of a string

The exact spacetime metric representing the exterior of a static cylindrically symmetric string is found. The geometry is conical, with a deficit angle of 8, where is the linear energy density of the string. The results of Vilenkin, obtained using linearized gravity, are thus shown to be correct to all orders in G. Strings with G (1/4) are found to collapse the exterior spacetime, resulting in dimensional reduction.