Quantum stress tensor at the Cauchy horizon of Reissner-Nordstr\"om-deSitter spacetime

TL;DR

This paper investigates the quantum stress tensor near the Cauchy horizon of Reissner-Nordström-de Sitter spacetime, confirming that quantum effects generally cause divergence, but the nature of the divergence can vary with parameters, impacting cosmic censorship.

Contribution

It provides a comprehensive parameter scan showing how quantum effects influence the divergence at the Cauchy horizon, extending previous limited analyses.

Findings

Quantum stress tensor diverges generically at the Cauchy horizon.

The sign of divergence can be altered by changing spacetime or field parameters.

Different types of singularities can occur depending on parameters.

Abstract

The strong cosmic censorship conjecture proposes that starting from generic initial data on some Cauchy surface, the solutions of the Einstein equation should not be extendable across the boundary of the domain of dependence of that surface. For the case of the Reissner-Nordstr\"om-de Sitter spacetime this means that any perturbation should blow up sufficiently badly when approaching this boundary, called the Cauchy horizon. However, recent results indicate that for highly charged black holes classical scalar perturbations allow for a violation of strong cosmic censorship. In a recent paper arXiv:1912.06047, two of us have argued that quantum effects will restore censorship for generic values of the black hole parameters. But, due to practical limitations, the precise form of the divergence was only calculated for a small number of parameters. Here we perform a thorough parameter scan using an alternative, more efficient semi-analytic method. Our analysis confirms arXiv:1912.06047 in the sense that the quantum stress tensor is found to diverge badly generically. However, the sign of the divergence can be changed by changing the mass of the field or the spacetime parameters, leading to a drastically different type of singularity on the Cauchy horizon.