  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.
