Is there a path of reasoning where Special Relativity **follows** from General Relativity?

Question

Usually, General Relativity textbooks start with Special Relativity, then come to the Einstein equations followed by some metrics and end up with cosmology.

I'm wondering: Is there a way back from General Relativity to Special Relativity?

Mass and Energy are equivalent. Relativistic masses (kinetic energies) add to the stress-energy-momentum tensor, don't they?

Is it possible to derive the formulas of Special Relativity (especially, the relativistic coefficient $\gamma$) out of the formulas of General Relativity? Is it done somewhere in the literature? Or could someone do it right here, in the answer?

(It's not a homework question, just curiousity!)

And, finally, if this can be done - what does that mean for special relativity? To me that would imply that somehow the curvature at the place of a fast-moving-object leads to time dilation and length contraction. Is that reasoning right?

What might be related to the question is the fact that Spacial Relativity describes how measurments of time and space (relatively) change if one changes from the viewpoint of one observer to the viewpoint of another oberver. Say, both at their trajectory in space-time. However, General Relativity describes how the field of curvature changes in space. Therefore, SR might be the calculations for "points", while GR is the calculations for "fields".

Another reading of my question: Can Special Relativity be regarded as an effect of General Relativity?

Answer 1

The answer is yes: Special Relativity can be derived from General Relativity. This is like asking whether the rules of geometry on a flat plane can be derived from the rules of geometry on a surface of any curvature. They can be derived because they are simply an especially simple application of those rules.

To address some other points in the question. Special Relativity is not General Relativity at a point, but it is what General Relativity becomes in a region in the vicinity of a given point.

Next, time dilation and Lorentz contraction are unrelated to spacetime curvature. They are present even if there is no spacetime curvature.