Free-falling motion of an elastic rigid rod towards a Schwarzschild black hole

We study the motion of an elastic rigid rod which is radially free-falling towards a Schwarzschild black hole. This is accomplished by reducing the corresponding free-boundary PDE problem to a sequence of ODEs, which we integrate numerically. Starting with a rod at rest, we show that it is possible to choose its initial compression profile so that its midpoint falls substantially faster, or slower, than a free-falling particle with the same initial conditions. This seems to be a purely kinematic effect, since on average there is no net transfer of elastic to mechanical energy.
Comment: 10 pages, 5 figures; v2: more details added, now 12 pages and 7 figures, matches final published version