What is a reference frame in General Relativity?
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.
Cite
@article{arxiv.2307.09338,
title = {What is a reference frame in General Relativity?},
author = {Nicola Bamonti},
journal= {arXiv preprint arXiv:2307.09338},
year = {2025}
}