The Poincaré-Einstein synchronization: historical aspects and new developments

An historical introduction to the Poincaré-Einstein synchronization and the problem of its transitivity is given. Inspired by cohomology theory I show that it is possible to improve the Poincaré-Einstein synchronization convention so as to obtain a consistent time foliation even in rotating frames for every assigned measure on space. This fact implies that there is, contrary to a widespread belief, a privileged time foliation of spacetime in several interesting cases.