Vacuum fluctuations outside cosmic strings

The vacuum stress-energy tensor for a conformal scalar field in the exterior spacetime of a straight cosmic string is calculated. The tensor is traceless, falls off as the fourth power of the distance from the string, and is proportional to the linear mass density of the string $c^2$μ/G in the physically reasonable case μ≪1. The linear energy density arising from the vacuum fluctuations is small compared with the linear mass-energy density of the string itself. A quasiregular singularity which appears in the exterior spacetime of a cosmic string with (1/4)<μ<(1/2) is shown to be unstable as a consequence of divergent vacuum fluctuations.