Of course you can transfer data through a gravitational wave. I had a long series of conversations about this with Rai Weiss (of LIGO fame) back in the mid 1980

Of course you can transfer data through a gravitational wave. I had a long series of conversations about this with Rai Weiss (of LIGO fame) back in the mid 1980's when I was an undergrad with a crazy idea to turn a cyclotron or synchrotron accelerator into a high frequency gravitational wave generator. The question isn't whether a wave can carry information, it's how you can modulate the carrier wave when the carrier wave is a gravitational wave generally requiring a pair of closely orbiting black holes to produce. I learned a ton of math and physics in the process of asking whether you could turn CERN or the superconducting supercollider into a gravitational wave generator, the most interesting being that conventional laboratory proposals for rotating bar gravitational wave generators and high frequency accelerator based gravitational wave generators are both in the end limited by the same quantity, the physical strength of materials. If you try to spin a bar faster than the point where its tip velocity is moving at roughly the speed of sound in the material, the bar will be ripped apart because the centrifugal force exceeds the tensile strength of the material, and if you try to increase the number of electrons or protons too high in the bundle being accelerated in your accelerator, you are similarly ultimately limited by the physical strength of the magnets responsible for bending the path of the particles into a circle. The other interesting observation is that the rotating bar obviously has a much higher mass (technically quadrature moment) than you can get circulating in an accelerator, but the angular velocity of the accelerator is so much higher and the exponent on the angular velocity term in the gravitational wave strain calculation is so high (fifth power? I forget, it's been many years) that the magnitudes of the strain producable in a laboratory setting by a rotating bar and by an accelerator are actually very close (and both, unfortunately, are too small to be of interest). When I went to grad school, my explicit interest was to build a tiny detector to look for high frequency gravitational waves on the grounds that if you wanted to communicate over Inter stellar or larger distances high frequency gravity waves were the best choice for avoiding the dispersion, scattering, and noise background that makes the the E/M spectrum a hard place to talk on long distances (essentially a variant on the SETI "watering hole" frequency choice but pushed into a different medium). I never had a design for a generator, but the idea was to build a table-top size Weber bar or laser interferometer tuned for the kind of high frequency waves you'd want to use for a communication system, and see if anybody happened to be talking on those channels.