Can a particle detector cross a Cauchy horizon?

TL;DR

This paper investigates whether a particle detector can cross a Cauchy horizon by analyzing its response in a black hole spacetime, revealing insights into horizon stability and quantum effects.

Contribution

It provides a detailed analysis of an Unruh-DeWitt detector's response near Cauchy horizons, focusing on the Reissner-Nordström black hole in the Hartle-Hawking state, highlighting quantum effects at horizons.

Findings

Detector response diverges at the Cauchy horizon

Quantum effects significantly influence horizon crossing

Differences observed between Cauchy horizon and singularity responses

Abstract

Cauchy horizons are well known to exhibit instabilities in classical spacetime dynamics and singularities in quantum field theory. We analyse the response of an Unruh-DeWitt particle detector that falls towards a Cauchy horizon, in terms of the specifics of the horizon, the choice of the quantum state and the specifics of the detector's trajectory. As a prototype, we study in detail the case for the $1+1$ Reissner-Nordstr\"om black hole with a scalar field in the Hartle-Hawking state. Comparisons are made with the response of a detector that falls into a Schwarzschild-like singularity.