How to Recover Spacetime Structure from Privileged Coordinates

TL;DR

This paper demonstrates that the geometric structure of any relativistic spacetime can be reconstructed from the transformation groups linked to specific privileged coordinate systems.

Contribution

It introduces a method to recover spacetime geometry solely from the symmetry groups of chosen coordinate systems, providing a new approach to understanding spacetime structure.

Findings

Spacetime geometry can be derived from transformation groups.

Privileged coordinates encode the geometric information.

The approach applies to arbitrary relativistic spacetimes.

Abstract

We show that the geometric structure of an arbitrary relativistic spacetime can be determined by the transformation groups associated with a collection of privileged coordinate systems.