What is a reference frame in General Relativity?

Nicola Bamonti

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arXiv · 2307.09338

What is a reference frame in General Relativity?

Nicola Bamonti

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Abstract

This work introduces a novel three-fold classification of reference frames in General Relativity, distinguishing between Idealised Reference Frames (IRFs), Dynamical Reference Frames (DRFs), and Real Reference Frames (RRFs). By defining a reference frame as a set of degrees of freedom instantiated by a physical system, the work contrasts this notion with that of coordinate systems-purely mathematical idealisations lacking physical instantiation. This classification addresses two longstanding challenges in GR: (P1) the difficulty of defining local and gauge-invariant observables, and (P2) how to interpret diffeomorphism gauge freedom in physical terms rather than as merely a mathematical redundancy. Overall, this work clarifies the conceptual foundations in classical General Relativity, enhancing our understanding of gauge-symmetries, observers and laying the groundwork for future investigations in both classical and quantum gravitational contexts.

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Nicola Bamonti. 2025-10-02. What is a reference frame in General Relativity?. https://arxiv.org/abs/2307.09338

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