The conformal transformation of the night sky

TL;DR

The paper provides a straightforward geometric proof that the night sky's appearance transforms conformally under observer change, independent of Lorentz transformations, and introduces a covariant expression for the conformal factor.

Contribution

It offers a simple, covariant geometric proof of the conformal transformation of the night sky that does not depend on spacetime dimensionality or Lorentz transformations.

Findings

The conformal transformation of the night sky is observer-independent.

A covariant expression for the conformal factor is derived.

In many cases, a thermal sky metric can be defined independently of the observer.

Abstract

We give a simple differential geometric proof of the conformal transformation of the night sky under change of observer. The proof does not rely on the four dimensionality of spacetime or on spinor methods. Furthermore, it really shows that the result does not depend on Lorentz transformations. This approach, by giving a transparent covariant expression to the conformal factor, shows that in most situations it is possible to define a thermal sky metric independent of the observer.