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I think it is easy to see that if gravitational waves can be created they can carry energy and can do work. Suppose we have a transverse-transverse wave generated by impinging on two masses close together. Let one mass A carry a stick which runs past touching the other B. I think I can show that the second in accelerating up and down will rub the stick, and therefore by friction make heat. I use coordinates physically natural to A, that is so at A there is flat space and no field (what are they called, "natural coordinates"?). Then Pirani at an earlier section gave an equation for the notion of a nearby particle, vector distance n from origin A, it went like, to 1 order in \eta \ddot{\eta}^{a} + R^{a}{}_{0b0} \eta^{b} =0 (a, b = 1,2,3) R is the curvature tensor calculated at A. Now we can figure R 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, \eta 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 A on the average, and to the wave amplitude.) Hence it rubs the stick, and generates heat.