When is it flat ? Is it when two observers are at mutual rest or is it when there is no presence of mass-energy ?

 

Is flat spactime an idealization (a limit as curvature tends to zero for the two above reasons)   and  is  curvature the "default" description?

 

Is the universal speed limit "responsible" for spacetime curvature or are they separate phenomena?

 

Do we need to specify "spacetime" curvature or does "curvature" or can we refer to it simply as "curvature" ?

1 hour ago, geordief said:

When is it flat ? Is it when two observers are at mutual rest or is it when there is no presence of mass-energy ?

It is the absence of mass-energy (or a completely even distribution of mass-energy). Speed doesn't affect it.

I think it is possible that space-time could be globally curved even in the absence of any mass or energy. For example, if the universe is finite then, for some topologies, this would mean it was curved (so that if you went off in one direction you would eventually end up where you started. (For some topologies, the universe can be finite but still flat.)

1 hour ago, geordief said:

Is flat spactime an idealization

It is an idealisation in that we are on the surface of the Earth (or, even in space, surrounded by massive bodies). So there is probably nowhere where there is no curvature at all (in the voids between galaxies, is the nearest you would get, I suppose).

1 hour ago, geordief said:

Do we need to specify "spacetime" curvature or does "curvature" or can we refer to it simply as "curvature" ?

If you are already talking about space-time, then I guess "curvature" is unambiguous by itself. Same as if you were talking about windscreens or bananas!