The renormalized stress-energy tensor for scalar fields in the Boulware state with applications to extremal black holes

TL;DR

This paper introduces a new mode-sum method to compute the renormalized stress-energy tensor for scalar fields in the Boulware vacuum, demonstrating its accuracy in extremal black hole spacetimes and exploring its implications for black hole stability.

Contribution

It generalizes the extended coordinate method to Boulware states and applies it to extremal black holes, revealing the RSET's regularity and effects on black hole structure.

Findings

RSET is regular at extremal horizons regardless of field mass and coupling

The method is accurate and efficient in Reissner-Nordström spacetimes

RSET perturbations can de-extremalize or eliminate black hole horizons

Abstract

We provide a mode-sum prescription to directly compute the renormalized stress-energy tensor (RSET) for scalar fields in the Boulware vacuum. The method generalizes the recently developed extended coordinate method which was previously only applicable to Hartle-Hawking states. We exhibit the accuracy and efficiency of the method by calculating the RSET in sub-extremal and extremal Reissner-Nordstr\"om spacetimes. We find numerical evidence for the regularity of the RSET at the extremal horizon regardless of the field mass and its coupling. We employ our numerical results of the RSET to source the semi-classical Einstein equations, demonstrating that if the RSET is considered as a static perturbation, it will either de-extremalize the black hole, or convert it into a horizonless object.