It has come up a few times in recent threads here that the energy conditions on the stress-energy tensor (weak, null, dominant, etc) traditionally used to prove global results (e.g. the singularity theorem, the positive energy theorem, geodesic motion theorems*) are problematic: they allow more than they should, yet prohibit physically plausible scenarios as well. It strikes me that the original motivation for these was the sense of 'generality' - the you don't need to assume a theory of matter. However, since this has not panned out so well, I ask: Does anyone know of attempts to re-prove such theorems on the basis of plausible constraints on the matter Lagrangian (or general forms of the Lagrangian) rather than the traditional energy conditions? ---- *There are papers proving rigorously that if you carefully take the limit as a body shrinks in size and mass, that it must follow a geodesic of the background geometry. Such theorems as I've seen must assume an energy condition as part of the proof. I have also seen a paper that shows that the energy conditions is *necessary*. That is, if you do the limiting process without any constraint on T, not only is non-geodesic motion possible, but even spacelike paths are possible. This is not really surprising given the possible properties of exotic matter.