Accurate Results of General Theory of Relativity

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sharma_satdev
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is it possible to get accurate results of general theory of relativity without discarding concept of three dimensional flat space
 
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I believe that the only way in keeping a flat spacetime and describing gravity geometrically is to use a flat embedding for our 4-dimensional spacetime. But I'm not an expert in this :)
 
In the weak field limit (e.g. no strong gravitational fields) we generally approximate space-time as flat, but I'm not sure if that's what you're asking.
 
This is how I see it.

General relativity relates the presence of energy-momentum to the curvature of space-time. From the curvature or space-time, we can compute time dilation and geodesics, which are phenomenon of study in GR.

You don't even need GR. Even in SR the flat 3-space must be embedded into a 4-dimensional Minowski space-time when we relate time with proper time and length with proper length.