Semiclassical effects induced by Aharonov-Bohm interaction between a cosmic string and a scalar field

In the context of the vacuum polarization effect, we consider the back-reaction of the energy-momentum tensor of a charged scalar field on the background metric of a cosmic string carrying a magnetic flux F. Working within the semiclassical approach to the Einstein equations we find the first-order (in ħ) metric associated to the magnetic flux cosmic string. We show that the contribution to the vacuum polarization effect coming from the Aharonov-Bohm interaction is larger than the one coming from the non-trivial gravitational interaction.