Vacuum polarization in the horizonless Bardeen metric

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 non-conformally 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.