Conformal Invariance of the Newtonian Weyl Tensor

TL;DR

This paper explores the conformal structure in Newtonian theories, demonstrating that the Newtonian Weyl tensor remains invariant under conformal transformations, analogous to relativistic spacetime properties.

Contribution

It introduces the Newtonian Weyl tensor and proves its invariance under conformal transformations, extending conformal invariance concepts to Newtonian gravity.

Findings

Newtonian Weyl tensor is conformally invariant.

Analogous conformal structures exist in Newtonian theories.

Provides a new geometric perspective on Newtonian gravity.

Abstract

It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.