Relativistic elasticity of rigid rods and strings. (English) Zbl 1308.83101
Summary: 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.
MSC:
| 83C57 | Black holes |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 83A05 | Special relativity |
| 35L05 | Wave equation |
Keywords:
relativistic elasticity; rigid rod; rigid string; car and garage paradox; Bell paradox; Schwarzschild black hole; Kruskal-Szekeres coordinates; wave equationReferences:
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