Well, Mr. Anonymous why not go to the man himself (i.e. Jason Lisle) and ask him his opinion on whether or not arbitrarily shaped and angled “light cones” introduces a gravitational field in the general case?
Here are a few pointers:
1. Jian Qi Shen says that X is frame dependent: An observer moving at constant velocity constitutes another frame.
2. Yes the Edwards space time is flat because the metrical tensor is not a function of position; therefore a simple conventional rescaling of the coordinates reestablishes the flat metrical tensor we are used to in ordinary special relativity. In this scenario ASC works.
3. But ASC fails to work with the asymmetric light cones that Jason is trying to introduce and whose skew varies from place to place: That is, Jason is telling us that the light cones in one direction are skewed toward us and in another completely different direction they are also skewed toward us – ergo, the skew changes from place to place; enter gravity.
4. Unfortunately Jian’s paper is only worked out for 2 dimensions; one spatial and one time. We find that the cat is really let out of the bag as soon as we move into 3 or 4 dimensions – it is then that your procedure of replacing r with x manifestly fails.
5. To simplify the problem you can forget all about moving observers; the gravitational fields become apparent between any two observers stationary with respect to one another but where one observer uses Jason’s skewed light cones and the other observer uses the standard vertical cones.