Clock synchronization for ring-riding observers on rotating disk

[cianfa72]

At the beginning of this thread we talked about 'stationary' congruence like the Langevin congruence in Minkowski spacetime. Langevin congruence is defined as stationary just because its worldlines are integral orbits of a timelike Killing vector field (KVF).

If the above is correct then, by definition, given a spacetime the existence of at least one stationary congruence suffices to define it as a stationary spacetime, right ?

 

[PeterDonis]

by definition, given a spacetime the existence of at least one stationary congruence suffices to define it as a stationary spacetime, right ?

Yes.

 

[cianfa72]

So in Minkowski spacetime there are some types of timelike KVFs (actually an infinite families of them): inertial KVFs, Rindler KVFs and Langevin KVFs (the corresponding integral orbits define indeed stationary congruences). Both the first two are also static since they are hypersurface orthogonal whilst the third is not.

 

[PeterDonis]

So in Minkowski spacetime there are some types of timelike KVFs (actually an infinite families of them): inertial KVFs, Rindler KVFs and Langevin KVFs (the corresponding integral orbits define indeed stationary congruences). Both the first two are also static since they are hypersurface orthogonal whilst the third is not.

Yes. Note, however, that while the inertial KVFs are timelike everywhere, the others are not; they are only timelike in restricted open regions of the spacetime (in the Rindler case, the appropriate "wedges" where the hyperbolas that are the integral curves of the KVF are timelike; in the Langevin case, an open "tube" where the radius is small enough to make the helical integral curves of the KVF timelike).