Take a ring of some material (in my thinking its likely a construct of some compact gravitational solution, like a Kerr singularity with a >> m).
This ring is rotating a some huge speed, with a frequency of nu_e.
Along comes an incident regular gravitational wave, with the roughly same frequency as the rotation of the structure, nu_w ~ nu_e.
What will happen?
Look at what happens with the ring (which is assumed at least somewhat pliable and soft), is not spinning.
The gravity wave simply interacts with it causing a change in its shape from circular to an ellipse.
Make the ring a spinning entity, – (so that the dots above are rotating) and what happens: The ring becomes an emitter of gravitational radiation – it scatters the incoming waves.
Why – well its easy to imagine that the ring has some properties like tension and stiffness, due to rotation. Then as the ring is turning its shape shifting will turn with the ring, making a new gravitational emitter. In other words the ring gets deformed, rotates to a new position, and then un-deforms – radiating the gravitational energy it has stored.
With systems like this in the normal world, we know that when the frequencies of the spinning object is comparable to the frequency of the incoming radiation, we get resonant tuning – the ring will maximally scatter incoming radiation.
What are the numbers?
Looking at energy radiated, need to start over again, but
10-60 watts. Is that enough for an electron?