Vacuum polarization for lukewarm black holes

TL;DR

This paper calculates the quantum scalar field's vacuum polarization on lukewarm black holes, demonstrating regularity at horizons through numerical and analytical methods.

Contribution

It provides the first detailed computation of vacuum polarization for lukewarm black holes, combining numerical and analytical approaches to show horizon regularity.

Findings

Renormalized expectation value is regular at both horizons.

Numerical calculations confirm regularity of the quantum field.

Analytical approximation supports numerical results.

Abstract

We compute the renormalized expectation value of the square of a quantum scalar field on a Reissner-Nordstrom-de Sitter black hole in which the temperatures of the event and cosmological horizons are equal (`lukewarm' black hole). Our numerical calculations for a thermal state at the same temperature as the two horizons indicate that this renormalized expectation value is regular on both the event and cosmological horizons. We are able to show analytically, using an approximation for the field modes near the horizons, that this is indeed the case.