Unruh-DeWitt detector response along static and circular-geodesic trajectories for Schwarzschild–anti-de Sitter black holes

We present novel methods to numerically address the problem of characterizing the response of particle detectors in curved spacetimes. These methods allow for the integration of the Wightman function, at least in principle, in rather general backgrounds. In particular we will use this tool to further understand the nature of conformal massless scalar Hawking radiation from a Schwarzschild black hole in anti–de Sitter space. We do that by studying an Unruh-DeWitt detector at rest above the horizon and in circular-geodesic orbit. The method allows us to see that the response rate shows peaks at certain characteristic frequencies, which correspond to the quasinormal modes of the spacetime. It is in principle possible to apply these techniques to more complicated and interesting physical scenarios, e.g., geodesic infall or multiple detector entanglement evolution, or the study of the behavior of quantum correlations in spacetimes with black hole horizons