About Synchronisation of Clocks in Free Fall Around a Central Body

The conventional nature of synchronisation is discussed in inertial frames, where it is found that theories using diierent synchronisations are experimentally equivalent to special relativ-ity. In contrary, in accelerated systems only a theory maintaining an absolute simultaneity is consistent with the natural behaviour of clocks. The principle of equivalence is discussed, and it is found that any synchronisation can be used locally in a freely falling frame. Whatever the choosen synchronisation, the rst derivatives of the metric tensor disapear and a geodesic is locally a straight line. But it is shown that only a synchronisation maintaining an absolute simultaneity allows to deene time consistently on circular orbits of a Schwarzschild metric.