Yes, that is the one I meant. I get your objection now.Third, the last metric on the mathpages page, where the acceleration does not vary with position, would seem to be a better one to describe "uniform" acceleration, at least in the sense that Einstein was talking about in his thought experiments on the subject. However, as you can see, the metric in this form is both time-dependent and non-diagonal; after reading that page, I think that feature is what was behind my intuitive guess in an earlier post about "uniformly accelerating coordinates" raising issues.
Yes. It kind of follows from the EP that that a "globally uniform gravitational acceleration" is equivalent to an uniformly accelerating frame in flat space-time.For example, if the curvature is zero everywhere, which it is in both the "Rindler metric" case and the "constant proper acceleration" metric (the last one on the mathpages page), then the geometry is flat Minkowski spacetime.
Yes, but the point of this example (off center spherical cavity) was merely to show that in an extended region of zero curvature , you still can have "gravitational acceleration" or "mass attraction".A final note: some of your examples don't have curvature zero everywhere, just in a particular region; but the geometry is still independent of which particular coordinate system is used to describe it.
Yes, which I guess answers the OPs question: Gravitational acceleration is "fictitious" in GR.So the general point that the laws of physics should be written in terms of things like curvature, not things like "gravitational acceleration", still holds.)