Vacuum polarization in the horizonless Bardeen metric

TL;DR

This paper analyzes quantum vacuum fluctuations in a horizonless Bardeen spacetime, revealing significant differences based on coupling type and identifying potential instabilities beyond the weak-field approximation.

Contribution

It provides the first detailed computation of the renormalized stress-energy tensor in the Bardeen spacetime, highlighting the effects of coupling and stability issues.

Findings

Vacuum fluctuations differ markedly between conformally and nonconformally coupled fields.

At large distances, the behavior aligns with that in black hole and star backgrounds.

Certain parameters induce instabilities with exponential growth of fluctuations.

Abstract

We compute the renormalized stress-energy tensor for a massless quantum scalar field in the background of the horizonless Bardeen spacetime. Within the weak-field approximation, we show that the vacuum fluctuations differ significantly between conformally and nonconformally coupled fields, both in magnitude and in their behavior at short and intermediate distances. At large distances, we recover the universal asymptotic behavior previously observed in black hole and Newtonian star backgrounds. Going beyond the weak-field regime, we find that, for certain parameter ranges, the modes of the field can develop imaginary frequencies, leading to instabilities and an exponential growth of vacuum fluctuations. We also discuss critically the applicability of the anomaly-induced effective action for computing the renormalized stress-energy tensor in the conformally coupled case.