Can General Relativity stress-energy tensor be extended to include contributions from imaginary mass tachyons? what would be the expected gravitational coupling between tachyons and tardions?


Apparently the behavior of tachyons in general relativity has been analyzed, though I don't have information on your second question about couplings to tardyons. P. 127 of J. Richard Gott III's book Time Travel in Einstein's Universe, available on google books here, says:

A tachyon would have to be accompanied by gravitational waves, just as an airplane exceeding the speed of sound creates a sonic boom. In 1974, using a 1972 result found by F. C. Jones plus my own solution to Einstein's field equations for a tachyon in a different context, I found that a tachyon should emit a cone of gravitational radiation that would trail behind it. The emission would cause the tachyon to lose energy and, because of the hypothetical particle's peculiar nature, cause it to accelerate to still higher speeds. In keeping with Jones's insight, the particle's worldline through spacetime is bent like a wide arch. We would see the two sloping sides of the arch as a tachyon and an anti-tachyon approaching each other at just over the speed of light, going faster as they got very close, finally reaching infinite speed as they hit and annihilated each other at the top of the arch. After that, no more tachyon. Because tachyon world lines would bend in this way, tachyons would spend most of the time moving at just barely over light speed.

Based on this description, I suspect that in an asymptotically flat spacetime where we can find a coordinate system that's close to an inertial frame, from the perspective of such a frame the tachyon's worldline would look something like a hyperbola bounded by two sides of some event's past light cone, like the red curves in region IV of the Kruskal-Szekeres diagram here (from this page).

The references section on p. 269 indicates this paper by Gott was published in Astrophysical Journal 187 (1974): 1. This page shows the title as "A Time-Symmetric Matter, Antimatter, Tachyon Cosmology".

If you want to do further research, this pdf of a paper from the CERN document server gives "an exact solution of the Einstein-Maxwell equations" involving tachyons, and various papers on tachyons in general relativity are listed in the "references" section of papers like this one and this one. An interesting point made by the CERN paper is that when analyzing tachyons in general relativity, one doesn't need to make use of any concept of a tachyon "rest mass" so there are no imaginary quantities involved--see section 6 beginning on p. 15.


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