Observed Angles and Geodesic Light-Cone Coordinates

TL;DR

This paper clarifies how angles in Geodesic Light-Cone coordinates relate to observed angles, emphasizing the need for a tetrad and Cartesian coordinates for a global mapping on the sky.

Contribution

It demonstrates that observed angles in GLC coordinates cannot be fixed by gauge conditions alone and requires an observer-based tetrad and Cartesian system for proper identification.

Findings

Angles can be identified with observed ones in principle.

Gauge fixing alone is insufficient for global angle identification.

A tetrad and Cartesian coordinates are necessary for a consistent global map.

Abstract

We discuss the interpretation of the angles in the Geodesic Light-Cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always possible in principle, one cannot implement it in the usual gauge-fixing way, i.e. through a set of conditions on the GLC metric. Rather, one needs to invoke a tetrad at the observer and a Cartesian-like coordinate system in order to obtain the desired map globally on the observed sky.