Mode-sum prescription for renormalized expectation values for a charged quantum scalar field on a charged black hole

TL;DR

This paper introduces a new mode-sum method for efficiently calculating renormalized expectation values of a charged scalar field in static, spherically symmetric black hole spacetimes, exemplified on Reissner-Nordstrom black holes.

Contribution

A novel mode-sum prescription applicable to static, spherically symmetric spacetimes for computing renormalized quantum field expectation values.

Findings

Successfully computed scalar condensate, current, and stress-energy tensor for a charged scalar field.

Demonstrated the method on a Reissner-Nordstrom black hole background.

Provides a practical tool for quantum field calculations in curved spacetime.

Abstract

We present a new mode-sum prescription for the efficient computation of renormalized expectation values for a massive, charged, quantum scalar field propagating on a curved space-time background. Our method is applicable to any static, spherically-symmetric, four-dimensional space-time with a time-independent, background electrostatic potential and can be used to find the renormalized scalar condensate, current and stress-energy tensor. As an explicit example, we present a calculation of these quantities for a charged scalar field in the Hartle-Hawking state on a Reissner-Nordstrom black hole background.