Notes on Observational and Radar Coordinates for Localized Observers

The worldline of a uniformly accelerated localized observer in Minkowski space is restricted in the Rindler wedge, where the observer can in principle arrange experiments repeatedly, and the Cauchy problem for quantum fields in that Rindler wedge can be well defined. However, the observer can still receive the signals sourced by the events behind the past horizon, and coordinatize those events in terms of some kind of observational coordinates. We construct such observational coordinates in some simple cases with the localized observers in Minkowski, de Sitter, and Schwarzschild-like spacetimes, and compare them with radar coordinates for the same observers.