Rotating detectors in dS/AdS spacetimes

TL;DR

This paper investigates the behavior of uniformly accelerating and rotating detectors in de Sitter and anti-de Sitter spacetimes, revealing complex effects of curvature and rotation on detector response and periodicity properties.

Contribution

It introduces a detailed analysis of detector response in curved spacetimes with rotation, highlighting non-trivial effects of curvature on periodicity and thermality.

Findings

Periodic geodesic intervals depend on acceleration and rotation.

Detector response exhibits non-thermal features despite periodicity.

Curvature influences detector response through a perturbative expansion.

Abstract

We analyse several aspects of detectors with uniform acceleration $a$ and uniform rotation $\Omega$ in de Sitter ($\Lambda>0$) and anti-de Sitter ($\Lambda<0$) spacetimes, focusing particularly on the periodicity, in (Euclidean) proper time $\tau_{\rm traj}$, of geodesic interval $\tau_{\rm geod}$ between two events on the trajectory. For $\Lambda<0$, $\tau_{\rm geod}$ is periodic in ${\rm i} \tau_{\rm traj}$ for specific values of $a$ and $\Omega$. These results are used to obtain numerical plots for the response rate $\dot{\mathcal{F}}$ of Unruh-de Witt detectors, which display non-trivial combined effects of rotation and curvature through the dimensionless parameter $\Lambda c^2/\Omega^2$. In particular, periodicity does not imply thermality due to additional poles in the Wightman function away from the imaginary axis. We then present some results for stationary rotational motion in arbitrary curved spacetime, as a perturbative expansion in curvature.