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 8πGμ, where μ 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 Gμ. Strings with Gμ≥(1/4) are found to collapse the exterior spacetime, resulting in dimensional reduction.