- #36
PeterDonis
Mentor
- 47,011
- 23,432
zonde said:Asymptotically flat space time can be described using flat geometry.
Really? Then please exhibit, explicitly, such a description. Asymptotically flat is not the same as flat.
zonde said:You can't do that in GR because c is postulated to be always the same and valid geometries are restricted by this postulate.
Really? Why do you think so? It's true that *SR* postulates that c is always the same, but that's because SR only applies globally in a globally flat spacetime, including the postulate that "c is always the same". The rule that "nothing can go faster than light" in a curved spacetime must be generalized to "nothing can move outside the light cones", and the light cones in a curved spacetime can "tilt" from event to event, which is what gives the appearance of "c" changing. But all this can be perfectly well described by a geometry; it's just a curved geometry.
zonde said:Yes, that's the point. And because of that we can't say that GR satisfies relativity principle.
No, we can't say that a generic spacetime in GR is globally flat, which means a global Lorentz transformation can't possibly apply, since those only apply in globally flat spacetimes. An asymptotically flat spacetime, such as that around a single gravitating body, is not globally flat.
But we *can* describe a generic spacetime in GR using a curved geometry (*which* curved geometry depends on the specific spacetime), and we *can* describe any given curved geometry using various coordinate charts, and transform between them. We can also show that any physical observable in GR (such as the spacetime curvature observed around a given object by an observer traveling on a given worldline) is described by an invariant, something that is the same in all coordinate charts.
If you want to say that all this does not satisfy the "relativity principle", that's your choice of words, I guess, but it doesn't affect the physics. Basically you are trying to apply the rules of SR outside their domain of applicability; those rules only apply globally in a globally flat spacetime, and you are trying to apply them to a curved spacetime. That doesn't work.