Semiclassical Gravitational Effects in the Spacetime of a Magnetic Flux Cosmic String

It is well-known that some physical effects may arise in the spacetime of a straigth cosmic string due to its global conic properties. Among these effects, the vacuum polarization effect has been extensively studied in the litterature. In papers of reference [4] a more general situation has been considered in which the cosmic string carries a magnetic flux Φ and interacts with a charged scalar field. In this case, the vacuum polarization arises both via non-trivial gravitational interaction (i.e, the conical structure) and via Aharonov-Bohm interaction. In papers [4] the non vanishing VEV of the energy-momentum tensor of the scalar field were computed. However, this energy-momentum tensor should, in principle, be taken into account to determine the spacetime associated with the magnetic flux cosmic string. Using the