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 nongeodesic path of the reference frame.

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