  Local simultaneity conventions are mathematically represented by connections
on the bundle of timelike curves that defines the frame. Those simultaneity
conventions having an holonomy proportional to the Riemann tensor have a
special interest since they exhibit a good global behavior in the weak field
limit. By requiring that the simultaneity convention depends on the the
acceleration, vorticity vector and the angle between them we are able to
restrict considerably the allowed simultaneity conventions. In particular, we
focus our study on the simplest among the allowed conventions. It should be
preferred over Einstein's in flat spacetime and in general if the tidal force
between neighboring particles is weaker than the centrifugal force. It reduces
to the Einstein convention if the vectorial product between the acceleration
and the vorticity vector vanishes. We finally show how to use this convention
in practice.
