  We show that the equation of motion for a rigid one-dimensional elastic body
(i.e. a rod or string whose speed of sound is equal to the speed of light) in a
two-dimensional spacetime is simply the wave equation. We then solve this
equation in a few simple examples: a rigid rod colliding with an unmovable
wall, a rigid rod being pushed by a constant force, a rigid string whose
endpoints are simultaneously set in motion (seen as a special case of Bell's
spaceships paradox), and a radial rigid string that has partially crossed the
event horizon of a Schwarzschild black hole while still being held from the
outside.
