  The renormalized mean value of the corresponding components of the
Energy-Momentum tensor for massive scalar fields coupled to an arbitrary
gravitational field configuration having cylindrical symmetry are analytically
evaluated using the Schwinger-DeWitt approximation, up to second order in the
inverse mass value. The general results are employed to explicitly derive
compact analytical expressions for the Energy-Momentum tensor in the particular
background of the Black-String spacetime. In the case of the Black String
considered in this work, we proof that a violation of the weak energy condition
occur at the horizon of the space-time for values of the coupling constant,
that include as particular cases the most interesting of minimal and conformal
coupling.
