Vacuum polarization around stars: nonlocal approximation

TL;DR

This paper calculates quantum vacuum polarization effects around spherical stars, revealing dominant nonlocal contributions that modify the exterior metric and violate energy conditions, with implications for low-energy quantum gravity.

Contribution

It introduces a nonlocal approximation for vacuum polarization around stars, highlighting the importance of nonlocal effects over local ones in weak gravitational fields.

Findings

Nonlocal vacuum polarization dominates in the weak field limit.

Quantum corrections depend on the star's internal structure.

Vacuum polarization violates null energy conditions.

Abstract

We compute the vacuum polarization associated with quantum massless fields around stars with spherical symmetry. The nonlocal contribution to the vacuum polarization is dominant in the weak field limit, and induces quantum corrections to the exterior metric that depend on the inner structure of the star. It also violates the null energy conditions. We argue that similar results also hold in the low energy limit of quantum gravity. Previous calculations of the vacuum polarization in spherically symmetric spacetimes, based on local approximations, are not adequate for newtonian stars.