Consider this link :
http://www.ps.uci.edu/~superk/ , which says Neutrino has non-zero mass . So, particle Neutrino interacts gravitationally with other massive particles .
Consider Neutrino speed = c . This supports particle Neutrino does not cause frame-dragging . So , Lorentz Transformation & GR are not applicable to Neutrino ; as is observed in reality .
Only Newton's Laws are applicable to particle Neutrino .
Hansda, you are right the article(s) do say that the neutrino has non-zero mass, but they say nothing about how they interact gravitationally, aside from some speculation that they could contribute to the missing mass, dark matter. Note.., they do not say the neutrino IS dark matter.
What I have been trying to point out is that when discussing the neutrino, or other subatomic particles for that matter, gravity and/or frame-dragging, the discussion is completely speculative. There is no experimental evidence, observation or experience that involves neutrinos and either frame dragging or gravity.
The case here is one where we associate gravitation with mass, and then because we find that the neutrino and other subatomic particles have mass, we project or assume that they also interact as independent gravitational, point sources.
As I mentioned earlier, there have been experiments demonstrating that individual atoms interact gravitationally, in the same way that larger objects do. There is no observation of a neutrino interacting gravitationally with anything. We don't even have any experimental evidence that protons and neutrons, independently interact gravitationally. It is functionally difficult given our current technological limitations to design experiments, which can both control the other forces involved and measure the individual motion and interaction of these particles, we assume to be governed by gravitation.
Think about a neutrino for a moment. We can detect secondary particles that result from neutrino interactions with atoms. We can create neutrinos in high energy particle collisions. However, we cannot focus or change the direction of a neutrino's velocity after it has been created. We can't even detect all of the neutrinos created only the very small number that interact with atoms in the detector, providing us with secondary particle interactions we can detect.
Read back through the research papers. Though they are generally careful to explain all of the adjustments and controls required for the results they have obtained, they never say anything about adjusting the beam to account for any affect that gravity might have on the trajectory.
When you fire a gun or a missile over a long distance, you cannot aim it directly at the object you intend to hit. You must aim above it, to allow for how gravity will change its trajectory. This is not required for a neutrino beam. At least not over the distances involved in experiments we can conduct, today.
What it seems you are tring to do is project phenomena well described by general relativity, into an area of physics that general relativity does not explain. We do not currently have a successful quantum gravity model. There are some suggestions that involve inertia from a perspective of quantum mechanics, which if they could be or were confirmed might provide a better understanding of not just inertia, but of gravity at subatomic scales. However, should any of these be confirmed they would represent similar shifts in our understanding and interpretation of current theory, as would or will(?) the FTL neutrino data should it be confirmed.
If you want to extend frame-dragging and gravitation to neutrinos and subatomic particles, you must at the same time explain how general relativity works at those scales and resolve the conflicts between general relativity and quantum mechanis, that rise at those scales.
I do believe that there is a fundamental common origin for both GR and QM. I don't believe that how we interpret either will be entirely unaffected should we discover that common origin.
So, any current association of the neutrino and gravity or frame-dragging is speculation, unless or until you can explain the interaction in a manner consistent with QM.