[aroberge]

That is incorrect. What you describe is a dipolar oscillation. The simplest gravitational waves woudl have a quadrupole moment: stretch in one direction while contracting in the direction perpendicular to it. Have a look at https://en.wikipedia.org/wiki/Gravitational_wave where there is an animation illustrating the simplest case.

[marcosdumay]

Right. There are no dipolar gravity oscillation because of conservation of momentum, thus the waves must be quadrupolar.

Didn't think about that before.