Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-04-19
Class.Quant.Grav. 20 (2003) 2443-2456
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTeX, 9 pages, 2 figures, 1 table. Previous title "The gauge nature of simultaneity". Classical and Quantum Gravity http:/
Scientific paper
10.1088/0264-9381/20/11/332
Stationary extended frames in general relativity are considered. The requirement of stationarity allows to treat the spacetime as a principal fiber bundle over the one-dimensional group of time translations. Over this bundle a connection form establishes the simultaneity between neighboring events accordingly with the Einstein synchronization convention. The mathematics involved is that of gauge theories where a gauge choice is interpreted as a global simultaneity convention. Then simultaneity in non-stationary frames is investigated: it turns to be described by a gauge theory in a fiber bundle without structure group, the curvature being given by the Fr\"olicher-Nijenhuis bracket of the connection. The Bianchi identity of this gauge theory is a differential relation between the vorticity field and the acceleration field. In order for the simultaneity connection to be principal, a necessary and sufficient condition on the 4-velocity of the observers is given.
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