Conformal geodesics on vacuum space-times

TL;DR

This paper studies conformal geodesics in vacuum and warped space-times, deriving deviation equations and constructing smooth conformal Gauss coordinates on Schwarzschild-Kruskal space-time that extend to null infinity.

Contribution

It introduces a system of conformal deviation equations and demonstrates how to construct global conformal Gauss coordinates on Schwarzschild-Kruskal space-time.

Findings

Derived conformal deviation equations for vacuum space-times

Constructed smooth conformal Gauss coordinates extending to null infinity

Extended coordinate systems on Schwarzschild-Kruskal space-time

Abstract

We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.