Can a particle detector cross a Cauchy horizon?

Abstract

Cauchy horizons are well-known to exhibit instabilities in classical spacetime dynamics and singularities in quantum field theory. We analyze the response of an Unruh–DeWitt particle detector that falls toward 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–Nordström 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.