A New Formulation of General Relativity - Part I: Pre-Radar Charts as Generating Functions for Metric and Velocity

TL;DR

This paper introduces pre-radar charts as generating functions for the metric and velocity in an axiomatic formulation of general relativity, simplifying the theory while maintaining equivalence with traditional formulations.

Contribution

It proposes pre-radar charts as a new foundational tool that generate the metric and velocity fields, offering a simplified axiomatic approach to GR.

Findings

Pre-radar charts define an atlas for space-time.

They generate metric, velocity, and displacement fields.

Simplify the axiomatic formulation of GR.

Abstract

In this paper (Part I of a series of three papers) an axiomatic formulation of GR is given, here use is made of the concept of pre-radar charts. These charts have "infinitesimally" the same properties as the true radar charts used in space-time theory. Their existence in GR has far-reaching consequences which are discussed throughout the papers. For the sake of simplicity and convenience I consider only such material systems the state of which is defined by a velocity field, a mass density and a temperature field. But the main results hold also for more complex systems. It follows from the axiomatics that the pre-radar charts define an atlas for the space-time manifold and that, in addition, they generate the metric, the velocity field and the displacement of the matter. Therefore, they are called generating functions. They act like "potentials". At the end of the paper it is shown that the existence of pre-radar charts allows to simplify the original axiomatics drasticly. But the two versions of GR are equivalent.