For the record I make no claims about the title but I do get that impression from the paper “Algebraic stability analysis of constrain propagation” by Frauendiener and Vogel.
The paper provides a general introduction to how to perform analysis of the attractors of some dynamical system (with specified initial conditions) and then applies this to a particular initial value formulation of Einstein’s equations. The analysis turns out to be very complicated so two techniques are used; assume that the Christoffel symbols vanish and use numerical investigation. I find the initial results intriguing and worthy of more than a close second look.
They show that in order for the Constraint quantities to tend to zero in some numerical approximation various inequalities must be satisfied. These inequalities are linked directly to the geometrical formulation of the evolution scheme! Sections 6.2 and 6.3 give two common formulations of evolution schemes in Minkowski space and show that for only one of these schemes does violation of the constraint equations reduce over time. As it happens this turns out to be the hyperboloidal formulation, which I have a fondness for. The consequences are that for a numerical evolution of Einstein’s equations to behave nicely with respect to the evolution of the constraint quantities certain common choices must be avoided.
The paper does leave me with the feeling that this kind of topic hasn’t been looked at much. Moreover, since this is the first paper I’ve read about such things, my own comments should be taken with more than just a grain of salt. In any case I want more…