Noise Kernel for Self-similar Tolman Bondi Metric: Fluctuations on Cauchy Horizon

TL;DR

This paper calculates the Noise Kernel for a self-similar Tolman Bondi spacetime, revealing divergence at the Cauchy horizon which questions the stability of semiclassical predictions in naked singularity formation.

Contribution

It introduces a method to compute the Noise Kernel in self-similar Tolman Bondi metrics and analyzes its behavior near horizons, highlighting potential backreaction effects.

Findings

Noise Kernel diverges at the Cauchy horizon in naked singularity cases

Noise Kernel remains regular in covered singularity scenarios

Results suggest backreaction effects are significant near the Cauchy horizon

Abstract

We attempt to calculate the point separated Noise Kernel for self similar Tolman Bondi metric, using a method similar to that developed by Eftekharzadeh et. al for ultra-static spacetimes referring to the work by Page. In case of formation of a naked singularity, the Noise Kernel thus obtained is found to be regular except on the Cauchy horizon, where it diverges. The behavior of the noise in case of the formation of a covered singularity is found to be regular. This result seemingly renders back reaction non-negligible which questions the stability of the results obtained from the semiclassical treatment of the self similar Tolman Bondi metric.