Conformal Triality of the Kepler problem

TL;DR

This paper demonstrates that the Kepler problem can be understood as null geodesic motion within a conformally compactified Minkowski space, revealing a deep geometric connection with Minkowski, de Sitter, and Anti-de Sitter spaces.

Contribution

It establishes a conformal triality linking the Kepler problem to null geodesics on a compactified Minkowski space, offering a new geometric perspective.

Findings

Kepler problem is projectively equivalent to null geodesic motion.

Reveals conformal triality among Minkowski, dS, and AdS spaces.

Provides a geometric framework connecting classical mechanics and spacetime geometries.

Abstract

We show that the Kepler problem is projectively equivalent to null geodesic motion on the conformal compactification of Minkowski-4 space. This space realises the conformal triality of Minkwoski, dS and AdS spaces.