Rotating detectors in dS and AdS spacetimes

We analyze several aspects of detectors with uniform acceleration a and uniform rotation Ω in de Sitter (Λ>0) and anti--de Sitter (Λ<0) spacetimes, focusing particularly on the periodicity, in (Euclidean) proper time τₜᵣₐⱼ, of geodesic interval τgeod between two events on the trajectory. For Λ<0, τgeod is periodic in iτₜᵣₐⱼ for specific values of a and Ω. These results are used to obtain numerical plots for the response rate ̇ F of Unruh-DeWitt detectors, which display nontrivial combined effects of rotation and curvature through the dimensionless parameter Λc²/Ω². 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.