https://en.wikipedia.org/wiki/Gravity_gradiometry#Gravity_gr...
I reckon you might as well use neutrino's, they're easier to detect and easier to produce.
Remember how big and complicated LIGO and VIRGO are and that's to detect the loudest signals of that nature in the universe (at a very narrow frequency range)
I'm not sure why we'd want to even if we could, though I guess "hey look at this, I can push a black hole into another one" would likely be regarded as a rather meaningful kind of message on its own to anyone with the technology to hear it.
If you can do that, a lot of other civs are going to give you a wide berth. And some of the rest may consider you a problem.
[0] https://en.wikipedia.org/wiki/Graviton
[1] https://home.cern/science/physics/extra-dimensions-gravitons...