I want to add..
A lot of the analysis in Steven's paper is possible only because he was willing to re-derive some solutions working from first principles, to insert the higher order terms that get truncated in many textbook equations, and has for some time been exploring what it tells us when we do add in those higher-order terms. As I commented to Tom and John in a thread above; Steven worked through some things using pencil and paper - while on vacation, earlier this year - yielding some 30 pages of equations, without having a textbook for reference.
I think that people are scared of non-linearities, and would prefer to deal with 1st or 2nd order approximations that are linear, rather than trying to crack the Math of the actual Physics. I first heard this from Mikhail Kovalyov at FFP10, but since have heard it again and again from a retired local Physics prof who has lately become my mentor. The majority of non-linear equations are not soluble, so people typically make limiting assumptions that allow equations to be linearized, then solve those equations to see what salient behaviors are observed. They can plug in numbers, and test the results against reality.
However; this tends to obscure exactly all of the interesting behaviors we would like to look at, which allow us to see what these astronomical beasts really are. And that's where all the fun is! Seeing what's really there, and accurately describing it, is what this is all about. Without understanding the non-linear behaviors, we can never hope to really grasp what is going on in these objects, or whether it is best to say they are ECOs, MECOs, Dark Energy Stars, Gravatars, Black Holes, or something else entirely. Just calling something an AGN does not tell us about its nature.
But it is a daunting task to figure out the 2nd, 3rd, or 4th order terms that need to be re-inserted - that are missing from the textbook versions and describe the interesting dynamics - in order to see what is really happening.
All the Best,
Jonathan