What is a reference frame in General Relativity?

TL;DR

This paper proposes a new three-fold classification of reference frames in General Relativity, clarifying their physical and mathematical distinctions to address foundational issues related to observables and gauge freedom.

Contribution

It introduces a novel classification of reference frames in GR, linking physical systems to gauge-invariant observables and interpreting diffeomorphism gauge freedom conceptually.

Findings

Defines three types of reference frames: IRFs, DRFs, RRFs.

Addresses the challenge of gauge-invariant observables in GR.

Provides a conceptual interpretation of gauge freedom.

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.