Aether atmospheres http://arxiv.org/abs/1004.1467 claims to have an alternative explanation of the interaction of light around massive objects.

Many of the general-relativity-tests such as bending of light near a star and gravitational red/blue shift are explained without general-relativity & without Newtonian-approach. The authors first cast doubts on both, the Newtonian and the relativistic approach; and proposes a novel alternative-explanation. The new alternative explanation is based on refraction phenomenon of optics. Estimation of results with new approach are in agreement with known values. Though physics is different, but it is argued that general-relativity based gravitational-bending and refraction based bending have more in common than is generally realized. Also discussed are black-hole and gravitational-lensing in the new perspective of refraction. The new refraction-based theory makes a few new predictions and also suggest a few tests.

What are the errors in this paper?
 A: Without GR, there is no reason for clocks at higher elevations to desynch with clocks at sea level. In addition, GR models have had great success predicting the orbital precession of Mercury. (An earlier draft of this answer claimed that they were necessary to explain the 3:2 spin/orbit resonance of Mercury but that doesn't seem to be the case.) 
If you take these as strong evidence for general relativity, then all that the authors' works really buy you is the possibility for some extra "fudge factors" that have so far not been needed. (That is, their aether-atmospheres could be combined with general relativity to bend light more or less as the case may be.) Since they've not been needed, it's not a huge priority to investigate their influence.
It also looks like their explanations are a bit ad-hoc, as the aether atmospheres they want terminate at an arbitrary height (why?) and are made out of some form of exotic matter that somehow still interacts with light (what is it?).
Finally, some predictions seem to be off. For example, we have a lot of pictures of gravitational lensing, but they indicate that they should show off chromatic aberrations and color-dependent light shifting, ultimately providing rainbow-looking results. I've never seen a gravitational lensing photo which looks like this.
A: They seem to be making a very strong claim, that their theory can completely supplant GR. However, they only talk about optical observations. They never mention the many other tests of GR, such as solar system tests and the Hulse-Taylor system, and it doesn't seem plausible that their theory could explain these tests. Since the time when this paper was written, gravitational waves have also been directly detected, and these waveforms are extremely demanding tests of strong-field GR.
