Notes on observational and radar coordinates for localized observers

TL;DR

This paper explores how localized observers in various spacetimes can construct observational coordinates to describe events behind horizons, comparing them with radar coordinates to understand their observational framework.

Contribution

It introduces a method to construct observational coordinates for localized observers in Minkowski, de Sitter, and Schwarzschild-like spacetimes, and compares them with radar coordinates.

Findings

Observational coordinates can be constructed for localized observers in different spacetimes.

Comparison shows differences and similarities between observational and radar coordinates.

Provides a framework for understanding signals from behind horizons in various spacetimes.

Abstract

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.