It's not very practical. We've been able to detect gravitational waves from black holes (or maybe neutron stars? Something like that anyways...) falling into each other, so in theory we could send a message across the galaxy using non-electromagnetic means if we could deliberately cause a similar event.
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.
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.