Inspired by the gravtiomagnetic analogy, I would expect that just as a charged tachyon would emit normal (electromagetic) Cerenkov radiation, any mass-carrying warp drive would emit gravitational Cerenkov radiation. The gravitomagnetic approximation may well break down near the mass, but "sufficiently far" from it, this would still be valid. Is that correct?
Specifically, let's suppose there is a moving closed surface S, such that on and outside S the gravitomagnetic equations are approximately valid (no assumptions about interior), such that it moves with a velocity greater than $c$, and such that it "carries mass", in the sense that the closed surface intergral of the gravitational field strength around S is negative (net inward gravitational field).
In general relativity, is this situation even possible? If so, would it emit gravitational radiation? If so, how fast would it lose energy (mass)?
I am motivated by the recent media hype around the Alcubierre metric. Nevertheless, it is a general question applying to any proposed "moving warp bubble" solution of general relativity. (As opposed to, say, a pair of "stargates", or a "warp corridor", or whatever -- if a mass $M$ travels through a stargate, it might be that the gate through which it enters could get heavier by $M$, and the gate through which it leaves could get lighter by $M$. Then this particular question wouldn't arise.)