# Global GR theorems without energy conditions?

1. Jul 5, 2011

### PAllen

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?

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*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.

2. Jul 5, 2011

### PAllen

I found a paper on this theme:

http://arxiv.org/abs/1012.6038

This specifically addresses the issue of scalar fields which are a thorn in the side of the energy conditions.

3. Jul 5, 2011

### bcrowell

Staff Emeritus
I think there are some cases where you can't re-prove the theorems because there are known counterexamples. For instance, the nonzero cosmological constant violates some energy conditions, and I think this means that certain inferences made in the past from CMB observations have had to be reanalyzed.