Nicola Bamonti

In General Relativity, the terms ‘reference frame’ and ‘coordinate system’ must be distinguished. The former refers to physical systems that are dynamically coupled with the gravitational field, aside from possible approximations, while the latter refers to a set of mathematical variables that are representative artefacts. This necessary distinction is lost in pre-general relativistic physics, where we can choose as a reference frame a system of real physical objects that is not affected and cannot affect the physical system under consideration. Therefore, we can make it coincide with a coordinate system without the need for approximations. We propose a a novel three-fold distinction between three types of reference frames, considered as material systems. In particular, we discern between Idealised Reference Frames, Dynamical Reference Frames and Real Reference Frames, depending on their increasing physical role in the total dynamics. Using a Bianchi I model in Minisuperspace, we give a cosmological example of the use of a gravitational Dynamical Reference Frame, namely a reference frame constructed with gravitational degrees of freedom in the standard case where the gravitational stress-energy tensor is not defined in the Einstein field equations. We also analyse the role of active and passive diffeomorphisms in changing a reference frame.