Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker universe

Abstract

We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes [($1+1$)-dimensional Schwarzschild metric and near-horizon effective metric for any stationary black hole in arbitrary dimensions] as well as a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. For black holes, the trajectories are defined in Schwarzschild coordinates, and the field modes correspond to a Boulware vacuum, whereas for the FLRW case, the detector is moving along the path defined in original cosmic time and the field modes are related to a conformal vacuum. The analysis is done for three stages (de Sitter, radiation dominated, and matter dominated) of the universe. We find that, although the detector is freely falling, it registered particles in the above-mentioned respective vacuums. We confirm this by different approaches. The detection probability distributions, in all situations, are thermal in nature.