Wrong again. "Einstein's GR" is exactly the same as modern GR. How could it be any different if the same field equations are used !
Yes, and this is
exactly what GR is. It models space-time, with world lines in it, at all places and all times. And since space-time is in general curved, so are the world lines. Our human senses can only perceive "slices" of that space-time, hence the illusion of movement and progression of time. In reality though space-time is static, and so are the world lines of all particles in it; but those world lines are
curved in accordance with the geometry of the underlying space-time itself. It is precisely this relationship that GR describes. In doing so GR is a completely deterministic model, which is why it is so hard to reconcile it with quantum physics which is probabilistic in nature.
This is a complete non-sequitur, and you yourself have explained why. Space-time is not just the collection of all points, but the collection of all
events; hence it contains all points of a ray of light at all times. It simply becomes a static curve in four dimensions, of which we see "a slice at a time", like a movie in a cinema. The entire movie is on the reel, but you cannot see it in its entirety at once. The rate of progression of this "movie" is determined by the causal structure of space-time - each two events are separated not only spatially, but also in time, and that separation is exactly 1 second every 300,000km, which is constant for all observers. Therefore it is obvious that, when space-time is curved, so is the null geodesic which is traced out by light. It is a natural consequence of a curved space-time. No artificial mechanisms such as changes in permittivity and permeability of the vacuum are required or called for. The vacuum is exactly the same for all observers.
This is just plain wrong. Here is the original publication by Einstein of his GR field equations :
http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=6E3MAXK4&step=thumb
He explicitly talks about space-time, its curvature, and how it is mathematically derived. He also explicitly states that GR does
not make any predictions about processes in nature other than gravity, and says that he was wrong on this point in previous publications. The entire article contains
no mention whatsoever of a varying speed of light. Go figure.
I had given this references previously, but you never replied to it.
Of course not. It's
space-time, not space. They are not the same. GR deals with space-time, as clarified by Einstein in his above publication, and by the very simple fact that all indices in the tensor equation run 0...3.
Yet you cannot show us where in the EFEs this relation for varying speeds of light is hidden, and nowhere is this mentioned in Einstein's publication of the field equations. Furthermore, your variable speed of light does
not actually explain any gravitational interactions, like perihelion precession, frame dragging, the n-body problem etc etc. It is simply nonsense.
What complete and utter nonsense. GR says nothing about "wave nature of matter", or it being the cause of objects falling down. No such things appears anywhere in GR, and they make no physical sense at all.