Quantization of massive scalar fields over static black string backgrounds

TL;DR

This paper analytically evaluates the energy-momentum tensor of massive scalar fields in static black string backgrounds using the Schwinger-DeWitt approximation, revealing violations of the weak energy condition at the horizon.

Contribution

It provides explicit analytical expressions for the energy-momentum tensor of massive scalar fields in black string spacetimes, including effects of different coupling constants.

Findings

Violations of the weak energy condition occur at the horizon.

Analytical expressions are derived for the energy-momentum tensor in black string backgrounds.

The results include cases of minimal and conformal coupling.

Abstract

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.