[pushkar (OP)]

can the results of general theory of relativity be accurately derived without discarding the concept of Euclidean flat space


MOD EDIT - Please make the subject a question.

[graham.d]

Which results? Many results of GR cannot be derived explicitly at all because the equations that result are too complex and have no analytical solution, even with simple metrics. Many "results" can be observed via numerical analysis on suitably powerfiul computers though. This does not give so much insight perhaps but does produce answers.

[Farsight]

I don't think so, pushkar. There's a paper called Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime which is interesting, see http://adsabs.harvard.edu/abs/2008ChPhL..25.1571Y. This is more reasonable than people generally appreciate, because Einstein did talk about inhomogeneous space and curvilinear motion rather than curved spacetime per se:

"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..."

But there is an issue. When you move away from the idea of curved spacetime and think in terms of inhomogeneous space instead, you find that you need something to cause this inhomogeneity. Then you find yourself with curved space, and all you've done is swapped one geometry for another.

[lightarrow]

can the results of general theory of relativity be accurately derived without discarding the concept of Euclidean flat space

*Space* could be flat in a *curved* spacetime. You intended exactly "space" or "spacetime"?