Those who claim being PhDs in physics while unable to calculate kinetic energy.

Gravity communication? Well, because gravitational waves (GW) move with c, there is no advantage in term of speed. (There is advantage in passing via huge masses without absorption hovever.)

The problem using GW is that they are VERY AND VERY VEAK (it has a mathematical reason - gravitational radiation is not a dipole like the electromagnetic one but a quadrupole radiation). We even can not detect radiation of spiraling neutron stars or black holes - events requiring energies equivalent to the rest mass energy of entire Sun burnt completely into gravitational radiation in a few seconds flash. (Imagine the RATE of energy conversion during these few seconds: E/t - it is even MORE than entire Milky Way galaxy light power). Yet we can not detect such "powerful" gravitational radiation by a sensitive detectors a few thousand light-years away.

So, gravitons carry so little energy that communication by them seems to be unrealistic.