Reissner Nordstr\"{o}m Background Metric in Dynamical Co-ordinates: Exceptional Behaviour of Hadamard States

TL;DR

This paper investigates the semiclassical behavior of the Reissner-Nordström black hole in a dynamical coordinate system, revealing differences from dust collapse models and analyzing the stability and quantum effects near horizons and singularities.

Contribution

It introduces a coordinate system for Reissner-Nordström solutions that captures dynamical evolution and examines the global validity of Wald axioms with Hadamard states, comparing semiclassical effects to dust collapse.

Findings

Divergence on the Cauchy horizon confirmed

Semiclassical domain extends up to the Cauchy horizon

Backreaction is significant near the central singularity

Abstract

We cast the Reissner Nordstrom solution in a particular co-ordinate system which shows dynamical evolution from initial data. The initial data for the $E<M$ case is regular. This procedure enables us to treat the metric as a collapse to a singularity. It also implies that one may assume Wald axioms to be valid globally in the Cauchy development, especially when Hadamard states are chosen. We can thus compare the semiclassical behaviour with spherical dust case, looking upon the metric as well as state specific information as evolution from initial data. We first recover the divergence on the Cauchy horizon obtained earlier. We point out that the semiclassical domain extends right upto the Cauchy horizon. This is different from the spherical dust case where the quantum gravity domain sets in before. We also find that the backreaction is not negligible near the central singularity, unlike the dust case. Apart from these differences, the Reissner Nordstrom solution has a similarity with dust in that it is stable over a considerable period of time. The features appearing dust collapse mentioned above were suggested to be generally applicable within spherical symmetry. Reissner Nordstrom background (along with the quantum state) generated from initial data, is shown not to reproduce them.