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So, my question is a pretty basic one. How do we construct the right coordinate systems for doing the "equivalent" windowless room thought experiments? Specifically:

In the gravitational/accelerated non-inertial frame what is the form of the gravitational field (as a function of position)?

If the field is a non-constant function of position then how is it considered either uniform or flat?

How are simultaneity, distance, and time experimentally defined in the uniform field?

What is the correct transformation between the accelerated and an inertial frame?

Can you simply use the Lorentz transform to boost between observers with uniform (non-inertial) motion in the gravitational field? (i.e. since spactime is flat do four-vectors still transform like usual, especially the four-momentum)

Any other hints would be appreciated.