# Vacuum polarization of the quantized massive scalar field in the global monopole spacetime II: the renormalized quantum stress energy tensor

## TL;DR

This paper calculates the renormalized quantum stress-energy tensor for a massive scalar field in a global monopole spacetime using the Schwinger-DeWitt approximation, revealing violations of energy conditions.

## Contribution

It provides a detailed derivation of the quantum stress-energy tensor for arbitrary coupling in a global monopole background, extending previous work with a second-order approximation.

## Key findings

- Quantum scalar field violates energy conditions in this spacetime.
- Results applicable to minimal and conformal coupling cases.
- Uses Schwinger-DeWitt approximation up to second order.

## Abstract

This paper is devoted to the construction of the renormalized quantum stress energy tensor $\left<T_{\mu}^{\nu}\right>_{ren}$ for a massive scalar field with arbitrary coupling to the gravitational field of a pointlike global monopole, using the Schwinger-DeWitt approximation, up to second order in the inverse mass $\mu$ of the field. The given stress energy tensor is constructed by functional differentiation with respect to the metric tensor of the one-loop effective action of sufficiently massive scalar field, such that the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results are obtained for a general curvature coupling parameter $\xi$, and specified to the more physical cases of minimal and conformal coupling, showing that in this specific cases, the quantum massive scalar field in the global monopole spacetime violates all the pointwise energy conditions.