Dear Cristinel,
Thanks for reminding me that the Weyl tensor (with 10 independent components) can be thought of as containing the information of the Riemann tensor (20 independent components) minus that of the Ricci tensor (10 independent components). So in the case of the vanishing Ricci, Riemann=Weyl.
I have tried to establish that space and `what fills space' are not two different entities. That is, by considering space means considering the accompanying fields as well. That the matter fields are present in the metric (without taking recourse to the energy-stress tensor), can also be proved by the conventional belief which considers singularity as the source of curvature in the absence of the energy-stress tensor. For this reason, I have considered Kasner, Kerr, Schwarzschild solutions. (For this purpose, I argue that if the source matter is present at the epoch of singularity, it must also be present at other times. That is, the source matter is already present through the metric field, in the Kasner solution.)
However, we must understand that the singularity is not the sole representative of curvature (in the absence of energy-stress tensor), since the conventional wisdom cannot explain the curvature of the Ozsvath-Schuckling solution (which is singularity-free). Hence the metric field (which has been shown to contain matter and gravitational energy in three cases) must be the real source of curvature.
Another reason, why the singularity is not an efficient representative of curvature, is the controversial character of the singularity (black hole) in the Schwarzschild solution. There are claims that the black hole mass must be zero [Narlikar & Padmanabhan, Foundations of Physics, Vol. 18, pp.659-668 (2008)].
The interpretation of the Schwarzschild solution, as a spacetime structure sufficiently away (of course that will be out of the event horizon) from some mass, is fine. In this case, the curvature present at those points can only be explained in terms of the gravitational energy (recalling that GR is a local theory). This is what I have emphasized in the essay.
The parallel you mention between the GR cases and the electromagnetic one, is interesting. Thanks. It may contain important information.
___Ram