I Detecting Gravitational Waves & Alcubierre Drive

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I saw a conference from a Ligo physicist she said they are detecting gravitation wave of collapsing star. I also read the Doppler effect is working on gravity due to limited speed (c). I want to know if it is possible to detect a big mass traveling close to the speed of light in ours frame of reference using Ligo or a similar interferometer?
 
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Only accelerated masses can radiate gravitational waves. In principle the launch or deceleration of such a spacecraft might be detectable but keep in mind the scale of the events LIGO/VIRGO need to see something: Several solar masses getting accelerated to relativistic speeds in a few milliseconds.
 
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