Noise Kernel for Reissner Nordstrom Metric: Results at Cauchy Horizon

TL;DR

This paper calculates the quantum stress tensor fluctuations near the Cauchy Horizon in Reissner Nordström spacetime, revealing distinct behaviors from other models and providing insights into semiclassical gravity during gravitational collapse.

Contribution

It introduces the point-separated Noise Kernel for Reissner Nordström spacetime and compares its behavior at the Cauchy Horizon with other models, highlighting unique fluctuation characteristics.

Findings

Noise Kernel behavior differs from Tolman Bondi metric at the Cauchy Horizon.

Quantum stress tensor fluctuations do not diverge in the same way as in previous models.

Stress tensor fluctuations exhibit distinct patterns for naked singularity and black hole end states.

Abstract

We obtain point separated Noise Kernel for the Reissner Nordstr\"{o}m metric.The Noise Kernel defines the fluctuations of the quantum stress tensor and is of central importance to Semiclassical Stochastic Gravity.The metric is modeled as gravitationally collapsing spacetime, by using suitable coordinate transformations, defined earlier. The fluctuations of the quantum stress tensor, at the final stage of collapse are then analysed for both, the naked singularity and black hole end states. The behavior of this Noise Kernel, at the Cauchy Horizon for naked singularity shows markedly different behaviour from self similar Tolman Bondi metric, which was obtained earlier. In the latter a very unique divergence was seen, which does not appear for the Reissner Nordstr\"{o}m metric, here . It is known that the quantum stress tensor itself, diverges at the Cauchy Horizon (CH) for both of these metrics . In contrast, it can now be seen that the the fluctuations of the stress tensor behave differently for the two cases. We give a discussion and further directions for investigations of this interesting behaviour in the two cases (regarding the collapse scenario).