Gravitational effect of the quantum vacuum outside a cosmic string
The conical geometry of a static cylindrically symmetric cosmic string gives a non-vanishing contribution to the vacuum expectation value of the energy-momentum tensor of a quantum field. Here we construct a model of a cosmic string taking into account the gravitational field of this energy density. The strongly curved interior of the string is modelled by a homogeneous fluid with vanishing tangential and radial stress. The integrated effect of vacuum polarization in this region is assumed to be accounted for by a singular layer with a traceless energy-momentum surface density at the surface of the string. The total Tolman mass of the system is positive, so the string produces an attractive gravitational field.