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.
Keywords
Cite
@article{arxiv.1406.0634,
title = {Relativistic elasticity of rigid rods and strings},
author = {Jose Natario},
journal= {arXiv preprint arXiv:1406.0634},
year = {2019}
}
Comments
20 pages, 8 figures; v2: typos corrected, figure added, some points clarified, matches final published version; v3: typos in the references fixed