Unruh--DeWitt detectors in spherically symmetric dynamical space-times

TL;DR

This paper investigates the thermal properties of spherically symmetric dynamical space-times using Unruh--DeWitt detectors, comparing semi-classical and quantum field methods, and exploring implications for cosmological horizons and temperature interpretation.

Contribution

It introduces the use of Unruh--DeWitt detectors in dynamical space-times and compares their responses with semi-classical methods, revealing limitations in associating surface gravity with temperature in cosmological settings.

Findings

Static black hole and de Sitter cases show consistent thermal interpretations.

In realistic cosmological models, detector responses do not exhibit Boltzmann-like thermal behavior.

Surface gravity may not directly correspond to temperature in dynamical cosmological horizons.

Abstract

In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein--de Sitter universe (that is a more realistic situation in the frame of $\Lambda$CDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.