Relativistic elasticity of rigid rods and strings

Abstract

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.

20 pages, 8 figures; v2: typos corrected, figure added, some points clarified, matches final published version; v3: typos in the references fixed

References in corpus (3)

• Static self-gravitating elastic bodies in Einstein gravity
• Dynamics of Bianchi type I elastic spacetimes
• Spherically symmetric steady states of John elastic bodies in general relativity

Cited by in corpus (7)

• Frequency spectrum of an optical resonator in a curved spacetime
• Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process
• Elastic shocks in relativistic rigid rods and balls
• Free-falling motion of an elastic rigid rod towards a Schwarzschild black hole
• Rigid elastic solids in relativity
• String loop vibration around Schwarzschild black hole
• Relativistic elastic membranes: rotating disks and Dyson spheres