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Whether I understand properly or not:

In an arbitrary space-time (with an arbitrary curvature) in any sufficiently little region we can go to Local Inertial Frame of Reference - sit into the free falling lift. Being there our experiments are the same as we have in SR.

But if I have some mysterious device like a voltmeter where instead of volts there are Riemann curvature tensor valus measuered along its scale....

What this device will show me? Of course it should show me non-zero curvature tensor values???

So on the one hand I think that I am in SR (in flat space-time) since my experiments in free falling lift are the same as in SR, but when I look on my "curvature-meter" device it shows me that there are non-zero tensor components...

If I have similar device called "metric-tensor-meter" it should show me the Minkovski values... correct ?