Renormalized stress-energy tensor for scalar fields in Hartle-Hawking, Boulware and Unruh states in the Reissner-Nordstr\"om spacetime

TL;DR

This paper calculates the renormalized stress-energy tensor for a quantum scalar field in various states around Reissner-Nordström black holes, using a novel Euclidean technique, and compares results with existing analytical approximations.

Contribution

It introduces an efficient Euclidean method for renormalizing the stress-energy tensor in the Hartle-Hawking state and extends the analysis to Boulware and Unruh states for charged black holes.

Findings

Accurate stress-energy tensor calculations for different quantum states.

Validation of results against existing analytical approximations.

Analysis across a range of black hole charges and field parameters.

Abstract

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordstr\"om black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed ``extended coordinate'' prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a range of coupling constants and masses for the field and a range of electric charge values for the black hole, including near-extreme values. Lastly, we compare these results with the analytic approximations available in the literature.