Model for Gravity -- What mechanism distorts space in the real case?

[pervect]

These are interesting, but I would make one caution: the "sector model" approach helps to visualize spatial curvature, but that is not the same as spacetime curvature. And the difference can often be quite stark.

For example, consider the black hole example. The "sector models" visualizations show that the spatial curvature around a black hole is positive radially but negative tangentially. However, the spacetime curvature is the opposite: radially it is negative (geodesics diverge) while tangentially it is positive (geodesics converge).

So I think one has to be very careful with such pedagogical methods.

That is an issue, and while the author does explicitly address it, the solution does require a fairly advanced knowledge of special relativity.

To quote from the first paper: https://arxiv.org/pdf/1405.0323.pdf

In a spatial sector model a sector is rotated in order to lay it alongside the neighbouring sector. In the spatiotemporal case the rotation is replaced by a Lorentz transformation.

It's a step up from the proposal I often uses, saying that General relativity can be thought of as drawing space-time diagrams on "curved surfaces", going into much more detail about what is meant by a "curved surface". I always give that a very short shrift when I mention it, saying that a sphere is an example of what I mean by a curved surface and not attempting a more general defintion.

While the required knowledge of special relativity is a bit advanced, it's IMO more accessible and practical than trying to present differential geometry at the same intermediate level to the same audience.