Sorry? Why?Space is simply an artifact of time and the propagation of energy. Light travel time. Sorry, but the 2D rubber sheets really have to go.
The 2D rubber sheet and/or the analogy referenced in the OP, are just that, analogies. ALL analogies have limitations, and when those limitations are explained, they do a reasonable job in conveying what's going on.
The rest of your claims are convoluted to say the least, and not generally inferred. Space and time are co-ordinates that certainly are "related" and actually can be said to change within a BH.
http://www.einstein-online.info/spotlights/changing_places
http://arxiv.org/ftp/arxiv/papers/0705/0705.0941.pdf
Conclusions :
We have started with the light clock to derive time dilation, Doppler k-factor, addition of velocities, length contraction, Lorentz Transformations, invariance of spacetime interval. We specially tried to show that it is not difficult to deal with the spacetime coordinates in special relativity by manipulating their interrelations and interpreting a few simple events with the help of Minkowski diagram.
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