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In special relativity, we have a very intuitive idea of how observations work, there are global inertial frames as in classical mechanics, and to link one inertial observer to another, we simply use the Lorentz transform. I find this very intuitive, even though the concepts of absolute time and distance have been abandoned, the invariant interval makes up for that.

However, I have no idea how things are suppose to work in GR.

I understand that the equality between inertial mass and gravitational mass rules out any possibility for a global inertial frame, but that's where my intuition drops dead.

How are observers treated in GR?