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In this Wikipedia paragraph suggesting an explanation for the phenomenon of inertia, it claims:

Another physicist, Vern Smalley, has derived the Lorentz transformation for mass by assuming that the gravitational field identified by Einstein is distorted during acceleration. Einstein's assumption was that the field would not be deformed during acceleration, but Smalley explored what happened if it was. He found that during acceleration, the gravitational field of a mass was compressed in the direction of the acceleration and rarefied in the opposite direction. The gravitational field potential of the mass was already propagating at the speed of light, and by forcing the field to move faster, it was resisting the acceleration by resisting compression and rarefaction. This resistance to acceleration is what we call inertia. Throughout the process of acceleration, even up to the speed of light, the total quantity of gravitational field material remains constant, but the shape of the field identifies the inertial mass. ref: Smalley, "Deriving Mass Inertia and Time Interval Dilation."

Who is Vern Smalley?

But, more importantly, are there any good references on the "gravitational" curvature of spacetime of a moving mass being distorted due to special relativity?

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    $\begingroup$ I'm not sure if I accidentally put "general" relativity instead of "special" relativity in the title and description or if someone edited my question trying to be helpful. I really do mean distorted due to special relativity. In other words, the distortion seen when there is a relative velocity between the mass and observer because of the Lorentz transformation. $\endgroup$
    – user1744318
    Dec 14, 2013 at 21:13
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    $\begingroup$ Special relativity is central to this question. I don't understand why the special relativity tag continues to be removed from this question. $\endgroup$
    – user1744318
    Dec 14, 2013 at 21:17
  • $\begingroup$ I think the complaint is that the theory you are talking about is neither special relativity or general relativity, and people usually discuss alternate theories of gravity under the context of general relativity. $\endgroup$
    – Zo the Relativist
    Dec 14, 2013 at 21:27

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There is a solution to the Einstein equations which specifically models what happens when you put a massive, gravitating body and an observer into relative motion at relativistic speeds; the solution is called the Aichelburg-Sexl ultraboost. See here for the corresponding Wiki article :

http://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost

Unfortunately I am not very familiar with the physical and mathematical details of this metric, but perhaps you can use the above to at least point you into the right direction for some further research on the matter.

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