GR is invariant under general coordinate transformations. [it] If [/it] I understand correctly, this is basically devoid of any physical content. It just means that relabelling points does not change anything physical. So it's devoid fo physical content, right? On the other hand, in special relativity, the equations are covariant under Lorentz transformations. Those have physical content. without imposing this symmetry the speed of light would not be the same in all frames. My simple-minded question is: how is the Lorentz invariance ensured in GR? I used to think that it was somehow implemented as part of the general coordinate transformations but it seems now that I was completely in the left field. we should be able to recover special relativity from GR in the limit of a flat spacetime so the Lorentz symmetry must be present at some level in GR. But how is it implemented?