OnlyMe: forget it. You just can't talk to these guys. There's no sincerity, just a towering arrogance and ignorance that dismisses what Einstein said along with the patent evidence that he was absolutely right. And resorts to calling you a liar to boot, and slinging insults. I think it's shameful myself.
You are always quick with the "abuse & insult" card, but not so quick to address the points raised. Why do you not want to elaborate how exactly
$$\displaystyle{G_{\mu \nu }=\kappa T_{\mu \nu }}$$
has anything to do with a varying speed of light ? Obviously that is because it really doesn't, and deep down you know it; you are just too proud to admit that you have been wasting years making untenable assertions. I have shown on my GR primer thread how the field equations are derived, and what the meanings of the tensors are; I suggest you take a close look at it. It is obvious that it has nothing it all to do with varying light speeds.
The theory of differentiable manifolds was worked out long before Einstein came along; by the time he worked on developing GR, the meanings of the various tensors, like the Riemann tensor, the Ricci tensor, the metric tensor and the SEM tensor and so on, where all rigorously defined. Einstein made use of a language which was
already in existence, and it is clear that by publishing the above field equation ( which is a relation on manifolds between a curvature tensor and and energy tensor ) he was indeed talking about
space-time curvature, and not some nonsense about "inhomogeneous space" and "varying speed of light". If Einstein wanted to publish a theory about varying speeds of light and how that affects local clock rates and ruler measurements (??!), then he would have done so, but he didn't. He published a tensor equation involving
curvature tensors. There is no mention of changes in permittivity and permeability, nor is there any connection at all in the equations to the local speed of light. The tensors appearing in the EFEs have well defined, rigorous meanings, of which Einstein was perfectly aware. He used these geometric objects for a reason, and asserting anything else is simply intellectual dishonesty.
Now I suggest you at least consider the possibility that your understanding of things might not be correct, and go and do some study from one of the many good geometrodynamics textbooks. Perhaps then you see exactly where you went wrong. Remember, in this day and age of easy access to information, ignorance is indeed a choice.
patent evidence that he was absolutely right.
All evidence we have is entirely consistent with a curved space-time, which is exactly what Einstein was talking about; so yes, he
was absolutely right. Varying light speeds, on the other hand, fall down at even elementary hurdles, like light deflection.