Angular distances in metric theories

TL;DR

This paper derives a comprehensive, covariant formula for angular distances between point sources in any spacetime, incorporating effects like aberration and gravitational deflection, with explicit approximations for weak gravitational fields.

Contribution

It provides a rigorous, unified framework for calculating angular distances in general relativity, including finite-distance sources and various gravitational approximations.

Findings

Derived a general covariant expression for angular distance.

Unified treatment of aberration and gravitational deflection.

Explicit post-Newtonian and post-post-Minkowskian approximations.

Abstract

The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at a finite distance from the observer. The aberration and the gravitational deflection of light are treated in a unified way. Assuming the gravitational field to be weak, an explicit expansion of the angular separation within the post-post-Minkowskian approximation is carried out. The angular separation within the post-Newtonian approximation truncated at the order $1/c^3$ is straightforwardly derived.