Boulware Vacuum vs. Regularity: Thoughts on Anomaly-Induced Effective Action

TL;DR

This paper investigates the relationship between vacuum states and spacetime regularity in horizonless geometries, revealing that the preferred vacuum differs from the Boulware vacuum and is determined by anomaly-induced effective actions.

Contribution

It demonstrates how regularity conditions and anomaly-induced effective actions determine the appropriate vacuum state in horizonless spacetimes, challenging the traditional Boulware vacuum choice.

Findings

The regularity of spacetime and RSET dictate the vacuum state.

The preferred vacuum in Bardeen-type spacetime differs from Boulware.

A nontrivial vacuum with a distinct RSET profile is identified.

Abstract

We examine the vacuum state and its corresponding renormalized stress-energy tensor (RSET) in static horizonless regular spacetime in both two and four dimensions. Using the local field formulation of the anomaly-induced effective action, we show that the regularities of the spacetime and the RSET dictate the appropriate vacuum state. Furthermore, through a case study under the horizonless Bardeen-type spacetime, we demonstrate that the preferred vacuum state is not the Boulware vacuum, but a nontrivial one with a different RSET profile.