Physics is simple only when analyzed locally

TL;DR

This paper discusses how local analysis in General Relativity simplifies understanding by using congruences of world-lines, revealing the Newtonian force as a non-geodesic effect within a Minkowski-like local frame.

Contribution

It demonstrates how local splitting techniques in General Relativity clarify the emergence of Newtonian gravity and connect the 4D model with practical measurements.

Findings

Local reference frames can be constructed via congruences of world-lines.

Newtonian gravitational force appears as a non-geodesic effect in this framework.

Splitting techniques relate relativistic phenomena to Minkowski spacetime in measurements.

Abstract

The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special Relativity, thereby realizing the local description in terms of Minkowski spacetime in accordance with the equivalence principle. This approach holds promise for elucidating the foundational principles of relativistic gravitational physics, as it illustrates how its 4-dimensional mathematical model manifests in practical measurement processes conducted in both space and time. In addition, we show how, within this framework, the Newtonian gravitational force naturally emerges as an effect of the non-geodesic path of the reference frame.