Incorporation of special relativity into general relativity

I am writing a paper about SR and GR. I have the following:



Special relativity deals with inertial reference frames and flat space. General

relativity deals with accelerating reference frames and curved space. Inertial

reference frames are only an approximation that applies in a region that is small

enough for the curvature of space to be negligible, so the motion is rectilinear

and the rate of change of velocity can be considered to be 0.



So how do we incorporate SR into GR on a more general level (curved space,

acceleration, circular motion)? Empirically, we should be able to do this by

taking the SR equations from flat space and expressing them in tensor form.

Tensors possess the property that if they have a certain value in flat space,

then they will have the same value in any other coordinate system.



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Is my interpretation correct? "rate of change of velocity can be considered to be 0" bothers me.



I am trying to get a fundamental understanding without theheavy math.



Thanks