Vacuum Polarisation and the Black Hole Singularity

TL;DR

This paper investigates how vacuum polarisation influences mass inflation singularities inside charged black holes, revealing that quantum effects intensify the singularity compared to classical predictions.

Contribution

It provides an analytic approximation of the quantum backreaction on the mass function within a simplified charged black hole model, highlighting the impact of vacuum polarisation.

Findings

Vacuum polarisation amplifies the mass inflation singularity.

Analytic solutions are derived for the classical field equations.

Quantum effects lead to a stronger singularity than classical predictions.

Abstract

In order to investigate the effects of vacuum polarisation on mass inflation singularities, we study a simple toy model of a charged black hole with cross flowing radial null dust which is homogeneous in the black hole interior. In the region $r^2 \ll e^2$ we find an approximate analytic solution to the classical field equations. The renormalized stress-energy tensor is evaluated on this background and we find the vacuum polarisation backreaction corrections to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass function shows that the mass inflation singularity is much stronger in the presence of vacuum polarisation than in the classical case.