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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.)

Qmechanic
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Retarded Potential
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    @HDE226868: any stress-energy souce with a time-varying quadrupole moment will emit gravitational radiation. Certainly, the setting up and tearing down of the warp bubble would involve a time varying gravitational field involving (exotic) matter, so, genericically, I'd expect gravitational radiation. – Zo the Relativist Aug 18 '15 at 15:21
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    I do not understand why you resort to hypothetical tachyons to explain your question. Normal charged matter already does that when it moves faster through a medium than the speed of light in that medium (which is lower than the speed of light in a vacuum). – Sentry Jul 06 '16 at 16:55
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    @Sentry -- correct. But the question is about warp bubbles which are also "hypothetical" (to put it generously), so charged tachyons are appropriate, also "charged tachyons" is just two words :) – Retarded Potential Oct 03 '16 at 14:39
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    It doesn't emit gravitational Cerenkov, but if you put it in an isotropic photon field (e.g. CMB) you can show that it emits a kind of electromagnetic Cerenkov. Actually for most simple designs, it emits so much radiation so quickly that it is more of a bomb than a form of (hypothetically) viable travel. – Base Apr 25 '17 at 15:54
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    why call it Cerenkov radiation? is there a medium where the gravitational waves travel with velocity lower than velocity of light in vacuum? That is the basic problem that has to be answered with this question imo, and the question is talking of "velocity greater then c" !!! whatever it is, if it is, it is not Cerenkov radiation – anna v Jun 04 '18 at 05:34

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Let's take a look of the gravitational field of particles travelling at the speed of light in relativity. These are called gravitational shock-waves and they carry a space-time shock that travels with them at the exact same wave-front. However, as can be seen from the consideration of the work of Aichelburg and Sexl (1971), this shock is just the information about a point mass attracting you for a fleeting (shocking) moment. Specifically, it carries no energy transfer in the same sense as the Newtonian gravitational field of e.g. a meteor flying by also does not transfer any net energy.

It is attractive to think about the shock plane getting deformed into a Cherenkov-like shock cone as you breach the speed of light, but there is really no exact solution to support that. This is because relativity is built in a way so that if you put physical sources into a space-time, they must fulfill their dynamical equations, otherwise the space-time knows and rewards you with absolutely unpleasant singularities. And there is really no known physical dynamics that would get you to and beyond the speed of light.

So let's take a look at linearized relativity. In linearized relativity you can make the sources do whatever you want and you don't have to pay for it the same way as in full nonlinear relativity. Then, if you take a pointlike source that is moving superluminally (following a space-like worldline), you can always transform into a frame in which the source is just a static spatial line. Static spatial lines are static and they do not radiate. If you boost back to your original frame, you will just feel gravitomagnetic-type effects doing funny stuff to you without making any work.

Finally, let's take a look at the Alcubierre warp drive published in 1994. In Alcubierre's original proposal, the metric sees no naughty asymptotics. In fact, the Alcubierre metric goes to zero exponentially because Alcubierre wrote it down so that it does. So observers far away do not even know that a warp drive gravitationally is or was there. Alcubierre checked what makes the space-time behave like that only afterwards from the Einstein equations. If there is radiation, you can magick it away with fairy dust (the matter source of the Alcubierre metric), if you need radiation, you can magick it in. So I do not know what to take from that but no, there is no radiation in the proposed metric.

In summary. No, there is no gravitational Cherenkov radiation in relativity. Then again, who knows what can fairy dust do.

Void
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The basic metric for the Alcubierre drive is asymptotically flat (it reduces to flat space as $r \rightarrow \infty$). Hence the far field for the metric will be flat so no emission of gravitational waves. Nothing actually goes faster than light in there (indeed, in the ideal case, the spaceship doesn't even move at all)

Slereah
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    Asymptotic flatness doesn't force zero gravitational radiation. The metric for a binary black hole system is asymptotically flat, too, after all. – Zo the Relativist Aug 18 '15 at 15:22
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    @JerrySchirmer: True. However, in the case of the Alcubierre metric, the fall-off to flatness is exponential in the original coordinates, which kills all the orders in the multipole expansion. For this reason, there are no gravitational waves emitted in the metric, which is what the answer probably meant. – Alexey Bobrick May 29 '21 at 15:07
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a warp bubble in general relativity is when you compress space in front of you and expand space behind you by pumping energy into the space in front of you and negative energy into the space behind you. Therefore you are moving space around you not moving through space allowing you to effectively hack your way around the universal speed limit because your not actually moving. so no you would not generate chrenkov radiation because this requires that you travel faster than the phase velocity of light in that medium. or I guess fastre than the phase velocity of gravity in your question....?

Lab DLS
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