On the definition of a reference frame and the associated space in a general spacetime
Abstract
A reference frame F can be defined as an equivalence class of spacetime charts (coordinate systems) having a common domain U and exchanging by a spatial coordinate change. The associated physical space is made of the world lines having constant space coordinates in any chart of the class. This is a local definition. The data of a global 4-velocity field v defines a global ''reference fluid". The associated global physical space is made of the maximal integral curves of that vector field. Assume that the local and global spaces correspond with the same three-dimensional network of observers. In that case, the local space can be identified with a part (an open subset) of the global space.
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