E Minguzzi 2003 Class. Quantum Grav. 20 2443 doi:10.1088/0264-9381/20/11/332
E Minguzzi
Show affiliationsStationary extended frames in general relativity are considered. The requirement of stationarity allows one to treat the spacetime as a principal fibre bundle over the one-dimensional group of time translations. Over this bundle a connection form establishes the simultaneity between neighbouring 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 out to be described by a gauge theory in a fibre bundle without structure group, the curvature being given by the Frölicher–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.
04.20.-q Classical general relativity
04.50.-h Higher-dimensional gravity and other theories of gravity
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
Issue 11 (7 June 2003)
Received 26 February 2003
Published 16 May 2003
E Minguzzi 2003 Class. Quantum Grav. 20 2443
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