is the curvature tensor calculated at . Now we can figure directly, it is not reasonable by coordinate transformation for it is the real curvature. It does not vanish for the transverse-transverse gravity wave but oscillates as the wave goes by. So, on the RHS is sensibly constant, so the equation says the particle vibrates up and down a little (with amplitude proportional to how far it is from on the average, and to the wave amplitude.) Hence it rubs the stick, and generates heat.
I heard the objection that maybe the gravity field makes the stick expand and contract too in such a way that there is no relative motion of particle and stick.
Incidentally masses put on opposite side of go in opposite directions. If I use 4 weights in a cross, the motions at a given phase are as in the figure:
Thus a quadrupole
Now the question is whether such a wave can be generated in the first place. First since it is a solution of the equations (approx.) it can probably be made. Second, when I tried to analyze from the field equations just what happens if we drive 4 masses in a quadrupole motion of masses like the figure above would do - even including the stress-energy tensor of the machinery which drives the weights, it was very hard to see how one could avoid having a quadrupole
I hesitated to say all this because I don't know if this was all known as I wasn't here at the session on gravity waves.