Quantum stress tensor for massive vector field in the space-time of a cylindrical black hole

The components of the renormalized quantum Energy-Momentum tensor for a massive vector field coupled to the gravitational field configuration of a static Black-String are analytically evaluated using the Schwinger-DeWitt approximation. The general results are employed to investigate the pointwise energy conditions for the quantized matter field, and it is shown that they are violated at some regions of the spacetime, in particular the horizon of the black hole.